Core Chapter 04 Excel Master 4th Edition Student
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Transcript of Core Chapter 04 Excel Master 4th Edition Student
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Ross, Westerfield, Jaffe, and Jordan's Excel Master
Corporate Finance: Core Principles and Applications, 4th edition
by Brad Jordan and Joe Smolira
Version 4.0
Chapter 4In these spreadsheets, you will learn how to use the follow
The following conventions are used in these spreadsheets:
FV
PV
Two-way data tables
RATE
NPER
FVSCHEDULE
NPV
EAR
APR
Exponential function
PV of an annuity
FV of an annuity
PMT
Annuity interest rate
Annuity periodsNested function
Annuity due
Loan amortization worksheet
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1) Given data in blue
2) Calculations in red
NOTE: Some functions used in these spreadsheets may require thatthe "Analysis ToolPak" or "Solver Add-In" be installed in Excel.
To install these, click on the Office button
then "Excel Options," "Add-Ins" and select
"Go." Check "Analysis ToolPak" and
"Solver Add-In," then click "OK."
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ing Excel functions:
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Chapter 4 - Section 2
The Multiperiod Case
Number of periods: 5
Initial investment: 500$
Interest rate per year: 7.0%
At the end of the investment, she will have: 701.28$
Initial investment: $500
Interest rate per year: 10%
Year
Beginning
Amount
Simple
Interest
Compound
Interest
Total
Interest
1 500.00$ 50.00$ -$ 50.00$
2 550.00 50.00 5.00 55.00
3 605.00 50.00 10.50 60.50
4 665.50 50.00 16.55 66.55
5 732.05 50.00 23.21 73.21Totals 250.00$ 55.26$ 305.26$
Year
Amount with
Simple
Interest
Total
Compound
Interest
So what does simple interest look like compared to compound interest? We can use Excel
simple interest and the total compound interest.
Excel contains numerous financial functions, many of which relate to the time value of mo
Suh-Pyng Ku has made the following deposit at the First National bank of Kent. How
As shown in the textbook, the future value of $1 is found by the equation FV = $1 (1 + r)
occurs with compound interest, not simple interest. To see the difference between simple
What is the value of the investment each year over the next 5 years? How much of the int
question with the following table:
Example 4.3: Interest on Interest
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1 550.00$ -$
2 600.00$ 5.00$
3 650.00$ 15.50$
4 700.00$ 32.05$
5 750.00$ 55.26$
RWJ Excel Tip
Number of
Periods 0% 5% 10% 15%
0 1.000 1.000 1.000 1.000
1 1.000 1.050 1.100 1.150
2 1.000 1.103 1.210 1.323
3 1.000 1.158 1.331 1.521
4 1.000 1.216 1.464 1.749
Interest Rate
Now we can graph the contribution of compounding to the future value of our investmen
To see the effect of compound interest, change the interest rate and see how the compou
To insert this bar chart, we highlighted the columns we wanted in the graph, went to the I
get the border shadowing effect, we right-clicked on the graph, selected Format Plot Area
In the past, future value tables were very common. Future value tables calculated the futu
a future value table relatively quickly in Excel. By the way, we will show you a much more
$-$5.00
$15.50
$-
$100
$200
$300
$400
$500
$600
$700
$800
$900
1 2 3
FutureV
alue($)
Time (years)
Future Value, Simple Interest, and C
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5 1.000 1.276 1.611 2.011
6 1.000 1.340 1.772 2.313
7 1.000 1.407 1.949 2.660
8 1.000 1.477 2.144 3.059
9 1.000 1.551 2.358 3.518
10 1.000 1.629 2.594 4.046
RWJ Excel Tip
Interest rate per year: 12%
There is a "bug" in Excel when graphing a table like the one above. If a table has text in th
graph. However, when the header row and column are numbers, Excel will not use the nu
in the legend and on the vertical axis, try the following: First, select just the data in the da
choose "Select Data." In the left hand column, highlight the data series you want to includ
allows you to choose the "Series Name." To include the number in the legend, simply sele
every column in the table. To include the column with the number of years as the horizonthe array that has the correct values for the horizontal axis.
Now that we have calculated the future value of a lump sum with the equation, we will us
investment opportunity:
An important fact about compound interest is that it results in exponential growth. To see
like this:
$0
$1
$2
$3
$4
$5
$6
$7
0 1 2 3 4 5
Futurevalueof$1
Time (years)
Future Value of $1 for Differ
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Number of years: 3
Initial investment: 400$
Future value: 561.97$
RWJ Excel Tip
Purchase price: 24$
Interest rate: 10%
Number of years: 387
Value today:
RWJ Excel Tip
How much will you have at the end of the investment. Using the FV function, we find that
To use the FV function, we entered the following:
The Rate is simply the interest rate, Nper is the number if periods, and Pv is the present v
detail later. Notice also that we put a negative sign in front of the present value. Excel wor
positive number we would have simply gotten a negative answer. Since we prefer our ans
Consider Peter Minuit's purchase of Manhattan Island from the American Indians. U
would that investment be worth today?
Example 4.6: How Much for That Island?
250,715,046,098,361,000.00$
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Bernard Dumas will receive a lump sum payment in the future. What is the value of t
Future value: 10,000$
Number of periods: 3
Interest rate: 8%
Present value: 7,938.32$
RWJ Excel Tip
To use the PV function, we entered the following:
Now that we have used the FV function, we will skip entering an equation to find the pres
syntax.
Two things about the above example. First, we did not want to change the column width f
display, we merged 3 cells by using the merge icon: In merging cells, you simply sel
that if you notice, the future value has all zeroes in the last three digits of the dollar amou
that while Excel is very precise, it only calculates to 15 significant digits. Although this gen
should consider if you are using very large or very small numbers.
If for some reason you do need more accurate calculations, www.precisioncalc.com has a
Present Value and Discounting
Example 4.7: Multiperiod Discounting
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Future value: 1$
Number of periods: 2
Interest rate: 9%
Present value: 0.8417$
RWJ Excel Tip
0.8417$ 0% 5% 10%
0 1.00000 1.00000 1.00000
1 1.00000 0.95238 0.90909
2 1.00000 0.90703 0.826453 1.00000 0.86384 0.75131
4 1.00000 0.82270 0.68301
5 1.00000 0.78353 0.62092
6 1.00000 0.74622 0.56447
7 1.00000 0.71068 0.51316
8 1.00000 0.67684 0.46651
9 1.00000 0.64461 0.42410
The Rate is simply the interest rate, Nper is the number of periods, and Fv is the future val
Notice also that we put a negative sign in front of the future value. Excel works like a calcu
number we would have simply gotten a negative answer. Since we prefer our answers to s
To set up a two-way data table, first create the rows and columns for the table. Next, in thcalculations in the cell. Next, select the cell with the equation you want to use in the data
enter the variables in your table that correspond to the row and column numbers you ent
Notice that Excel made our choices absolute references by default. Just hit OK and the dat
corner showing in this case, but remember we could hide this number by right-clicking, sel
semicolon.
Interest Rate
NumberofPeriod
s
Suppose we want to create a table with the present value factors for different interest ratup a basic PV problem, with $1 as the future value.
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RWJ Excel Tip
Finding the Interest Rate
Present value: 38,610$Future value: 50,000$
Number of periods: 3
Interest rate: 9.00%
RWJ Excel Tip
Example 4.8: Finding the Rate
To find the interest rate, we used the RATE function and entered the following:
A customer of Beatty Corp. wants to buy a tugboat today. Rather than paying immediately
charge to neither gain or lose on the sale?
Finding the interest rate necessary for a present value to reach a desired future value in a
We have the legend on the left hand side of the table running vertically. To do this, we me
Cells." Using the "Alignment" option, we moved the "Text" wheel to vertical.
Graphically, the present value factors look like this:
$-
$0.2000
$0.4000
$0.6000
$0.8000
$1.0000
$1.2000
1 2 3 4 5
Presentvalueof$1
Time (y
Present Value of $1 for Dif
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Finding the Number of Periods
Present value: 2,300,000$
Future value: 10,000,000$
Interest rate: 5%
Number of periods: 30.12
RWJ Excel Tip
NPER is the number of periods, Pv is the present value, and Fv is the present value. We lef
also that we put a negative sign in front of the present value. Excel works like a calculator i
and the future value negative.
Excel also has a built-in function to calculate the number of periods necessary for a lump s
You are saving up to buy the Godot Company and have the following information. How lo
To find the number of periods, we used the NPER function and entered the following:
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Future Value with Changing Interest Rates
Present value: 100$
Year Interest rate
1 8%
2 6%
3 10%
4 15%
5 11%
6 9%
Year
Value at
year end
1 108.00$
2 114.48
3 125.93
4 144.825 160.75
6 175.21
Future value: 175.21$
Rate is the interest rate, Pv is the present value, and Fv is the future value. We left the pa
put a negative sign in front of the present value. Excel works like a calculator in that it exp
value negative.
Suppose you are going to make a lump sum deposit today, and the interest rate you will rhave in 6 years?
One way to calculate the future value is to compound the value each year. In year 1, we w
calculate the future value in year 2 at the year 2 interest rate, and so on. Doing this, we fin
While this process is more repetitive than difficult, Excel has a function that will calculate
future value is:
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RWJ Excel Tip
t Cash flow
0 (50,000)$
1 25,000
2 20,000
3 15,000
Return: 7%
NPV: $3,077.73
RWJ Excel Tip
To calculate the NPV of the project using the NPV function, we entered the following:
Net Present Value
Example 4.10: NPV
Finance.com has the following investment opportunity for a new high-speed computer. Sh
In this function, Principal is the beginning deposit and Schedule is an array that contains t
Net present value is the present value of all outflows, plus the present value of all inflows.
present value.
To use the FVSCHEDULE, we entered:
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Interest rate: 12%
Salary
1 12,000,000$
2 12,000,000$
3 12,000,000$4 10,900,000$
5 10,900,000$
6 10,000,000$
7 9,000,000$
8 9,600,000$
9 9,000,000$
10 3,000,000$
11 3,000,000$
12 3,000,000$
Contract present value: $60,792,671.66
Notice one very important thing: We did not include the cash flow at time 0 in the NPV fu
did not truly create a function that calculated the NPV, but rather created a function that
cash flows, we use the NPV function to calculate the present value of the cash flows beyo
simply go to the NPV cell above.
We can use the NPV function to find the present value of any series of cash flows. For exa
text, we would do something like the following:
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Ending
Amount
Amount
with
Simple
Interest
550.00$ 550.00$
605.00 600.00
665.50 650.00
732.05 700.00
805.26 750.00
to draw a graph for us. First we need to set up a table that shows the value with
ney. We will begin by using equations before moving to Excel's functions.
much will she have at the end of her savings period?
t. In Excel, the carat ( ^ ) raises a number to a power. Of course, compounding only
interest and compound interest, consider the following example:
erest is simple interest and how much is compound interest? We will answer this
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20%
1.000
1.200
1.440
1.728
2.074
.
nd interest grows as the interest rate changes.
nsert tab, and then selected Column. We chose the 2-D Stacked Column option. To
and chose the Shadow option.
re interest factor for a variety of interest rates and time periods. We can construct
fficient method in the next section.
$32.05
$55.26
4 5
mpound Interest
Compound interest
Amount with simple interest
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2.488
2.986
3.583
4.300
5.160
6.192
header row and column, Excel will automatically use the text in the legend of the
bers in the legend, but rather include them in the graph. To include the numbers
a and ignore the header row and column. Next, right click on the entire chart and
e a legend for (Series 1, Series 2, etc.,) then select "Edit." This brings up a box that
t the cell that has the header you want to include. You will need to repeat this for
al axis, go to the "Horizontal (Category) Axis Labels," select "Edit", then highlight
e Excel's FV function to calculate the future value. Suppose you have the following
the exponential growth in practice, we can graph the future value table. It looks
6 7 8 9 10
nt Periods and Rates
0%
5%
10%
15%
20%
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you will have:
lue. We left the payment and type blank for now, but we will discuss this in more
ks like a calculator in that it expects cash flows. If we had left the present value as a
ers to show as positive, we entered a negative in front of the present value.
ing the FV function, if the purchase price of the island was invested, how much
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hat payment today?
nt value, but rather talk about the PV function. The PV syntax is similar to the FV
or the entire spreadsheet to display the future value. To get the future value to
ect the cells you want merged into one cell and click on the icon. The second thing is
nt and in the cents. You might think this is strange, and indeed it is. The reason is
rally does not create a problem in most calculations, it is something that you
add-in to Excel available that will calculate to 32,767 digits.
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15% 20%
1.00000 1.00000
0.86957 0.83333
0.75614 0.694440.65752 0.57870
0.57175 0.48225
0.49718 0.40188
0.43233 0.33490
0.37594 0.27908
0.32690 0.23257
0.28426 0.19381
ue. We left the payment and type blank for now, but we will discuss these later on.
lator in that it expects cash flows. If we had left the future value as a positive
how as positive, we entered a negative in front of the future value.
e upper left hand corner, enter the equation you would like to use into thetable, go to the Data tab, What-If Analysis, then Data Table. Excel will prompt you to
ered. For this data table , our entries were:
a table will be filled in automatically. We left the calculation in the upper left hand
ecting Format Cells, choosing Custom, and entering the custom type as a
es and periods. A two-way data table allows us to do this very easily. First, we'll set
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, he will pay at some point in the future. What interest rate would the Beatty Corp.
desired time period is a relatively simple problem using Excel.
rged the cells, typed in the text, right clicked on the cells and selected "Format
6 7 8 9 10
ears)
erent Periods and Rates
0%
5%
10%
15%
20%
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t the payment and type blank for now, but we will discuss these later on. Notice
in that it expects cash flows. We could have also made the present value positive
um today to reach a desired amount in the future.
g must you wait to buy the company?
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ment and type blank for now, but we will discuss these later on. Notice also that we
cts cash flows. We could have also made the present value positive and the future
ceive will change every year. With the following assumptions, how much will you
ill receive the year 1 interest rate. We will use the value at the end of year 1 to
d that the value each year is:
he future value of this amount. Using the FVSCHEDULE function, we find that the
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ould Finance.com make this investment? What is the net present value?
e interest rates for each period.
Unfortunately, as we will see, computer programmers don't understand net
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ction. The reason is simple. When the programmers created the NPV function, they
alculated the present value of cash flows. So, to calculate the NPV of a series of
d time 0, then add the cash flow at time zero to the result. To see how we did this,
ple, to find the present value of the Sidney Crosby contract we discussed in the
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Chapter 4 - Section 3
Compounding Periods
Example 4.11: EARs
APR: 24%
Compounding periods per year: 12
EAR: 26.82%
RWJ Excel Tip
Of course, you may have the EAR and need to find the APR. Remember that the APR is the legally quot
EAR: 18%
Compounding periods per year: 12
APR: 16.67%
Excel has functions to calculate the effective annual rate and the annual percentage rate.
Suppose Fernando Zapatero makes a deposit in an account with the following stated annual interest r
account?
To calculate the effective annual rate, we can use the EFFECT function as follows:
In the EFFECT function, Nominal_rate is the APR and Npery is the number of compounding periods per
As a lender, you know the interest rate and the number of compounding periods per year. In order to
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RWJ Excel Tip
APR: 5.50%
EAR: 5.65%
RWJ Excel Tip
To calculate the exponential function, we use EXP, found under the Math & Trig functions, as follows:
Example 4.14: Continuous Compounding
To calculate the annual percentage rate, we can use the NOMINAL function as follows:
In the NOMINAL function, Effect_rate is the EAR and Npery is the number of compounding periods per
Continuous Compounding
Excel does not have a function for continuous compounding, but it does have a function that calculate
Suppose Linda DeFond makes a deposit into an account with the following APR. The account has conti
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The sole argument of this Excel function is Number, which is the number we want to calculate the exp
this case. Since we are dealing with interest rates, we need to calculate the exponential function for th
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ed interest rate on loans.
te and compounding periods per year. What is the EAR of this
year.
arn this interest rate, what rate do you quote?
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year.
the exponential function (e ).
uous compounding. What is the EAR of this account?
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nential value. If you notice, the function returns 1.056540615 in
e interest rate and then subtract 1 (one.)
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Chapter 4 - Section 4
Simplifications
Present Value for Annuity Cash Flows
Annual payment: 50,000$Number of years for payments: 20
Interest rate: 8%
Present value: 490,907.37$
RWJ Excel Tip
Excel does not have built-in functions for perpetuities, growing perpetuities, or growing an
cell. We'll leave this up to you and instead concentrate on the broad array of annuity calcul
Example 4.19: Lottery Valuation
Finding the present value of an annuity is a simple task in Excel. Remember the Pmt argum
the annuity payment. Finding the present value of an annuity uses the PV function with the
Mark Young just won the state lottery and will receive the following set of equal payments
To find the present value of this annuity, we used the following arguments:
Rate is simply the interest rate, Nper is the number of periods, and Pmt is the annuity pay
negative sign in front of the payment. Excel works like a calculator in that one of the cash fl
payment as a positive number we would have gotten a negative answer. Since we prefer o
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Future Value for Annuities
Suppose you make the following deposits into a Roth IRA for retirement? How much will yo
Annual savings: 3,000$
Number of years to save: 30
Interest rate: 6%
Future value: 237,174.56$
RWJ Excel Tip
Rate is simply the interest rate, Nper is the number of periods, and Pmt is the annuity paynegative sign in front of the payment. Excel works like a calculator in that one of the cash fl
payment as a positive number we would have gotten a negative answer. Since we prefer o
The NPER and RATE functions can be used with the future value to find the number of peri
value.
Example 4.20: Retirement Investing
We can find the future value of an annuity using the Pmt argument in the FV function. Sup
will you have when you retire?
To find the future value of this annuity, we used the following arguments:
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Purchase price: 175,000$
Number of months for repayment: 240
Monthly interest rate: 0.50%
Monthly payment: 1,253.75$
RWJ Excel Tip
Retirement goal: 1,500,000$
Annual amount to save: 4,000$
Number of years to save: 35
Interest rate: 11.40%
Rate is simply the interest rate, Nper is the number of periods, and Pv is the present value.
sign in front of the present value. Excel works like a calculator in that one of the cash flows
present value as a positive number we would have gotten a negative answer. Since we pref
value.
To find the interest rate for an annuity, Excel uses the RATE function. Suppose you are savi
retirement balance. What interest rate is necessary for you to reach your goal?
Finding the Annuity Payment
Finding the Interest Rate
To find the annuity payment, Excel uses the PMT function. Suppose you are buying a house
To find the annuity payment, we used the following arguments:
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RWJ Excel Tip
Finding the Number of Payments
Amount owed: 3,000$
Monthly payment: 50$
Monthly interest rate: 1.50%
Number of months to pay off card: 154.65
Number of years to pay off card: 12.89
RWJ Excel Tip
To find the number of periods, we used the following arguments:
Nper is the number of periods, Pmt is the annuity payment, and Fv is the future value. Sinc
sign in front of the payment. Excel requires that one of the cash flows be positive and one
future value negative and would have received the same answer.
You ran a little short on your vacation, so you charged on your credit card. With the followi
To find the number of periods, Excel uses the NPER function.
To find the interest rate, we used the following arguments:
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Example 4.21 Delayed Annuities
Number of payments: 4
Amount of each payment: 500$
Date of first payment: 6Interest rate: 10%
First, we can find the present value of the annuity payments, which is:
Annuity present value: 1,584.93$
Value today: 984.12$
RWJ Excel Tip
Trick 1: A Delayed Annuity
Rate is the interest rate per period, Pmt is the annuity payment, and Pv is the present valu
negative sign in front of the payment. Excel requires that one of the cash flows be positive
the future value negative and would have received the same answer.
One of the tricks of annuities is getting the timing right. When we are dealing with a delay
Suppose Danielle Caravello will receive the following annuity payments. What is the value
Of course, we could solve this question with one calculation cell. Excel allows you to "nest"
calculation inside the present value of the lump sum without the intermediate step of calcu
results in a cleaner looking spreadsheet.
Now that we have the lump sum value, we can find the present value of the lump sum. We
the first payment, so we need to subtract one from the date of the first payment. So, the v
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Value today: 984.12$
Year Beginning
1 $ -
2 $ -3 $ -
4 $ -
5 -$
6 500$
7 500$
8 500$
9 500$
10 -$
Interest rate 10%
Value today: 984.12$
Trick 2: Annuity Due
Example 4.22: Annuity Due
Beginning of period annuity deposit: 50,000$
Number of years: 20
Interest rate: 8%
Present value: 530,179.96$
RWJ Excel Tip
So far, we have talked about ordinary annuities, that is, the payments occur at the end of t
the period.
To calculate the present value of an annuity due, we use the PV function and set the type o
Of course, there is another way to calculate the value of this annuity today. Suppose we se
With the cash flows set up like this, we can use the NPV function to find the value of the ca
Suppose Mark DeYoung, who won the lottery in a previous example, still wins the lottery b
winnings today?
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Example 4.23: Infrequent Annuities
Ann Chen is going to received the following annuity payments. What is the value of the pay
Annuity payment: 450$
Years between payments: 2
Years for payments: 20
EAR: 6%
Effective multi-year rate: 12.36%
Now we can use this rate to find the value today, which is:
Value today: 2,505.57$
Value today: 2,505.57$
Of course, we could always nest the functions to calculate the value today in one cell:
We can answer this problem in two steps. First, we need to find the effective rate for the y
In the FV and PV functions, the Type represents the payment type. If this argument is left b
entered, Excel uses beginning of period payments.
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uities. Each of these can be calculated by inputting the equations directly into a
ations in this section.
nt in the PV and FV functions that we left blank in Section 4.2? The Pmt stands for
annuity payment in the Pmt argument.
beginning one year from now. What is the value of the payments today?
ent. Since there is no present value, we left this blank. Notice also that we put a
ows must be positive and one of the cash flows must be negative. If we had left the
r answers to show as positive, we entered a negative in front of the payment.
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u have in your account when your golden years start?
ent. Since there is no present value, we left this blank. Notice also that we put aows must be positive and one of the cash flows must be negative. If we had left the
r answers to show as positive, we entered a negative in front of the payment.
ds or interest rate in the same manner we used these functions with the present
ose you are saving for retirement. Based on the following assumptions, how much
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Since there is no future value, we left this blank. Notice also that we put a negative
must be positive and one of the cash flows must be negative. If we had left the
er our answers to show as positive, we entered a negative in front of the present
g for retirement and know how much you will save every year, as well as a target
with the following terms. What is your monthly mortgage payment?
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there is no present value, we left this blank. Notice also that we put a negative
f the cash flows be negative. We could have made the payment positive and the
g assumptions, how long will it take you to pay off your credit card?
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. Since there is no future value, we left this blank. Notice also that we put a
nd one of the cash flows negative. We could have made the payment positive and
d annuity, there are a couple of ways to handle the calculation in Excel.
f the payments today?
one function inside another. Below, we nested the present value of the annuity
lating the present value of the annuity. Although this is a little more difficult, it also
also need to remember that the present value of an annuity is one period before
lue of the annuity today is:
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ments today?
ars between the annuity payments, which is:
lank or a 0 (zero) is entered, Excel uses end of period payments. If a 1 (one) is
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Chapter 4 - Section 5
Loan Amortization
Equal Principal Payment
Loan amount: 350,000$
Interest rate: 9%
This means that the equal annual principal payments will be:
Principal payments: 23,333.33$
So, the equal principal payment amortization table will look like this:
Beginning
Balance
Total
Payment
Interest
Paid
Principal
Payment
1 350,000.00$ 54,833.33$ 31,500.00$ 23,333.33$
2 326,666.67 52,733.33 29,400.00 23,333.33
3 303,333.33 50,633.33 27,300.00 23,333.33
4 280,000.00 48,533.33 25,200.00 23,333.33
5 256,666.67 46,433.33 23,100.00 23,333.33
6 233,333.33 44,333.33 21,000.00 23,333.337 210,000.00 42,233.33 18,900.00 23,333.33
8 186,666.67 40,133.33 16,800.00 23,333.33
9 163,333.33 38,033.33 14,700.00 23,333.33
10 140,000.00 35,933.33 12,600.00 23,333.33
11 116,666.67 33,833.33 10,500.00 23,333.33
12 93,333.33 31,733.33 8,400.00 23,333.33
13 70,000.00 29,633.33 6,300.00 23,333.33
14 46,666.67 27,533.33 4,200.00 23,333.33
15 23,333.33 25,433.33 2,100.00 23,333.33
Total 602,000.00$ 252,000.00$ 350,000.00$
RWJ Excel Tip
Amortization tables are an excellent application of Excel's abilities. Because an amortizati
fill in the rest of the amortization table. Suppose we have the following 15 year loan that r
To create the table, we first set up the header row and column. The beginning balance ref
earlier calculation of the principal payment, and the interest paid is the beginning balance
this for the second period, except that the beginning balance in period 2 is the ending bal
and interest rate, we can copy and paste the second row to fill in the table. To find the tot
sum button.
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Equal Payment
Loan amount: 350,000$
Interest rate: 9%
Equal payments: 43,420.61$
BeginningBalance
TotalPayment
InterestPaid
PrincipalPayment
1 350,000.00$ 43,420.61$ 31,500.00$ 11,920.61$
2 338,079.39 43,420.61 30,427.15 12,993.46
3 325,085.93 43,420.61 29,257.73 14,162.88
4 310,923.05 43,420.61 27,983.07 15,437.53
5 295,485.52 43,420.61 26,593.70 16,826.91
6 278,658.61 43,420.61 25,079.27 18,341.33
7 260,317.27 43,420.61 23,428.55 19,992.05
8 240,325.22 43,420.61 21,629.27 21,791.34
9 218,533.88 43,420.61 19,668.05 23,752.5610 194,781.32 43,420.61 17,530.32 25,890.29
11 168,891.03 43,420.61 15,200.19 28,220.42
12 140,670.61 43,420.61 12,660.35 30,760.25
13 109,910.36 43,420.61 9,891.93 33,528.68
14 76,381.68 43,420.61 6,874.35 36,546.26
15 39,835.42 43,420.61 3,585.19 39,835.42
651,309.13$ 301,309.13$ 350,000.00$
RWJ Excel Tip
To create the table, we first set up the header row and column. The beginning balance ref
calculation of the payment amount, the interest payment is the beginning balance multipl
is the total payment minus the interest paid. The ending balance is the beginning balance
that the beginning balance in period 2 is the ending balance in period 1. Since we have us
paste the second row to fill in the table. To find the total payments, total interest paymen
Creating an equal payment amortization schedule is similar to the equal principal amortiz
which we can calculate using the PMT function we discussed earlier. The loan payment wil
This means that the equal annual payments will be:
So, the equal annual payment amortization table will look like this:
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RWJ Excel Tip
"Balloon" or "Bullet" Loans
Suppose we have a commercial mortgage with the following characteristics. What will the
Loan amount: 100,000$
Amortization period (years): 20Time balloon payment due (years): 5
Payments per year: 12
Interest rate (APR): 12.00%
Monthly payment: 1,101.09$
Loan amortization tables are so common that Excel has a built-in worksheet to calculate a
select Insert, then the Spreadsheet Solutions tab. Below you will see the built-in spreadsh
Loan Amortization worksheet. We entered the values in the table at the top and the entir
Balloon loans are loans that are amortized over a relatively long schedule, but at some poi
going to be a little fancier here and set up the problem so that it works with any repayme
loan with the following characteristics:
Example 4.28: Partial Amortization, or "Bite the Bullet"
So, based on the original amortization schedule, the payments will be:
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Balloon payment: 91,744.33$
Balloon payment: 91,744.33$
The balloon payment is the present value of the remaining payments, so the balloon pay
Of course, we could have nested the functions to find the balloon payment as well like thi
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Ending
Balance
326,666.67$
303,333.33
280,000.00
256,666.67
233,333.33
210,000.00186,666.67
163,333.33
140,000.00
116,666.67
93,333.33
70,000.00
46,666.67
23,333.33
-
n table is repetitive, once we get the first couple of rows, we can copy and paste to
equires equal principal payments each year:
erences the loan amount, the principal payment is an absolute reference to the
multiplied by the interest rate (which is an absolute reference.) We then repeated
nce in period 1. Since we have used absolute references for the principal payment
al payments, total interest payments, and total principal payments, we used the
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EndingBalance
338,079.39$
325,085.93
310,923.05
295,485.52
278,658.61
260,317.27
240,325.22
218,533.88
194,781.32168,891.03
140,670.61
109,910.36
76,381.68
39,835.42
0.00
erenced the loan amount, the total payment is an absolute reference to the earlier
ied by the interest rate (which is an absolute reference,) and the principal payment
minus the principal payment. We then repeated this for the second period, except
d absolute references for the total payment and interest rate, we can copy and
ts, and total principal payments over the life of the loan, we used the sum button.
tion schedule. First, we need to calculate the loan payment for the 15 year loan,
l be:
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monthly payment be? How big will the balloon payment be?
loan amortization. To find this worksheet, right-click on one of the worksheet tabs,
et options. We selected the Loan Amortization worksheet and Excel inserted the
loan amortization table was constructed automatically.
nt during the life of the loan, the remaining principal of the loan is repaid. We are
t schedule, whether annually, monthly, or any other period. Suppose we have a
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ent will be:
:
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Loan Amortization Schedule
Loan amount 250,000.00$
Annual interest rate 3.10 % Sch
Loan period in years 30
Number of payments per year 12
Start date of loan 8/1/2013
Optional extra payments
Lender name:
Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
1 9/1/2013 250,000.00$ 1,067.54$ -$ 1,067.54$ 421.71$ 645.83$
2 10/1/2013 249,578.29$ 1,067.54$ -$ 1,067.54$ 422.80$ 644.74$
3 11/1/2013 249,155.50$ 1,067.54$ -$ 1,067.54$ 423.89$ 643.65$
4 12/1/2013 248,731.61$ 1,067.54$ -$ 1,067.54$ 424.98$ 642.56$
5 1/1/2014 248,306.62$ 1,067.54$ -$ 1,067.54$ 426.08$ 641.46$
6 2/1/2014 247,880.54$ 1,067.54$ -$ 1,067.54$ 427.18$ 640.36$
7 3/1/2014 247,453.36$ 1,067.54$ -$ 1,067.54$ 428.29$ 639.25$
8 4/1/2014 247,025.07$ 1,067.54$ -$ 1,067.54$ 429.39$ 638.15$
9 5/1/2014 246,595.68$ 1,067.54$ -$ 1,067.54$ 430.50$ 637.04$
10 6/1/2014 246,165.17$ 1,067.54$ -$ 1,067.54$ 431.61$ 635.93$ 11 7/1/2014 245,733.56$ 1,067.54$ -$ 1,067.54$ 432.73$ 634.81$
12 8/1/2014 245,300.83$ 1,067.54$ -$ 1,067.54$ 433.85$ 633.69$
13 9/1/2014 244,866.98$ 1,067.54$ -$ 1,067.54$ 434.97$ 632.57$
14 10/1/2014 244,432.02$ 1,067.54$ -$ 1,067.54$ 436.09$ 631.45$
15 11/1/2014 243,995.92$ 1,067.54$ -$ 1,067.54$ 437.22$ 630.32$
16 12/1/2014 243,558.71$ 1,067.54$ -$ 1,067.54$ 438.35$ 629.19$
17 1/1/2015 243,120.36$ 1,067.54$ -$ 1,067.54$ 439.48$ 628.06$
18 2/1/2015 242,680.88$ 1,067.54$ -$ 1,067.54$ 440.62$ 626.93$
19 3/1/2015 242,240.26$ 1,067.54$ -$ 1,067.54$ 441.75$ 625.79$
20 4/1/2015 241,798.51$ 1,067.54$ -$ 1,067.54$ 442.89$ 624.65$
21 5/1/2015 241,355.61$ 1,067.54$ -$ 1,067.54$ 444.04$ 623.50$
22 6/1/2015 240,911.58$ 1,067.54$ -$ 1,067.54$ 445.19$ 622.35$
23 7/1/2015 240,466.39$ 1,067.54$ -$ 1,067.54$ 446.34$ 621.20$
24 8/1/2015 240,020.05$ 1,067.54$ -$ 1,067.54$ 447.49$ 620.05$
25 9/1/2015 239,572.56$ 1,067.54$ -$ 1,067.54$ 448.65$ 618.90$
26 10/1/2015 239,123.92$ 1,067.54$ -$ 1,067.54$ 449.80$ 617.74$
27 11/1/2015 238,674.11$ 1,067.54$ -$ 1,067.54$ 450.97$ 616.57$
28 12/1/2015 238,223.15$ 1,067.54$ -$ 1,067.54$ 452.13$ 615.41$
29 1/1/2016 237,771.02$ 1,067.54$ -$ 1,067.54$ 453.30$ 614.24$
30 2/1/2016 237,317.72$ 1,067.54$ -$ 1,067.54$ 454.47$ 613.07$
31 3/1/2016 236,863.25$ 1,067.54$ -$ 1,067.54$ 455.64$ 611.90$
32 4/1/2016 236,407.60$ 1,067.54$ -$ 1,067.54$ 456.82$ 610.72$
33 5/1/2016 235,950.78$ 1,067.54$ -$ 1,067.54$ 458.00$ 609.54$
34 6/1/2016 235,492.78$ 1,067.54$ -$ 1,067.54$ 459.18$ 608.36$
35 7/1/2016 235,033.60$ 1,067.54$ -$ 1,067.54$ 460.37$ 607.17$
36 8/1/2016 234,573.23$ 1,067.54$ -$ 1,067.54$ 461.56$ 605.98$
37 9/1/2016 234,111.67$ 1,067.54$ -$ 1,067.54$ 462.75$ 604.79$
Enter values
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
38 10/1/2016 233,648.91$ 1,067.54$ -$ 1,067.54$ 463.95$ 603.59$
39 11/1/2016 233,184.96$ 1,067.54$ -$ 1,067.54$ 465.15$ 602.39$
40 12/1/2016 232,719.82$ 1,067.54$ -$ 1,067.54$ 466.35$ 601.19$
41 1/1/2017 232,253.47$ 1,067.54$ -$ 1,067.54$ 467.55$ 599.99$
42 2/1/2017 231,785.92$ 1,067.54$ -$ 1,067.54$ 468.76$ 598.78$
43 3/1/2017 231,317.16$ 1,067.54$ -$ 1,067.54$ 469.97$ 597.57$
44 4/1/2017 230,847.18$ 1,067.54$ -$ 1,067.54$ 471.19$ 596.36$
45 5/1/2017 230,376.00$ 1,067.54$ -$ 1,067.54$ 472.40$ 595.14$
46 6/1/2017 229,903.60$ 1,067.54$ -$ 1,067.54$ 473.62$ 593.92$ 47 7/1/2017 229,429.97$ 1,067.54$ -$ 1,067.54$ 474.85$ 592.69$
48 8/1/2017 228,955.13$ 1,067.54$ -$ 1,067.54$ 476.07$ 591.47$
49 9/1/2017 228,479.05$ 1,067.54$ -$ 1,067.54$ 477.30$ 590.24$
50 10/1/2017 228,001.75$ 1,067.54$ -$ 1,067.54$ 478.54$ 589.00$
51 11/1/2017 227,523.21$ 1,067.54$ -$ 1,067.54$ 479.77$ 587.77$
52 12/1/2017 227,043.44$ 1,067.54$ -$ 1,067.54$ 481.01$ 586.53$
53 1/1/2018 226,562.43$ 1,067.54$ -$ 1,067.54$ 482.25$ 585.29$
54 2/1/2018 226,080.17$ 1,067.54$ -$ 1,067.54$ 483.50$ 584.04$
55 3/1/2018 225,596.67$ 1,067.54$ -$ 1,067.54$ 484.75$ 582.79$
56 4/1/2018 225,111.92$ 1,067.54$ -$ 1,067.54$ 486.00$ 581.54$
57 5/1/2018 224,625.92$ 1,067.54$ -$ 1,067.54$ 487.26$ 580.28$
58 6/1/2018 224,138.66$ 1,067.54$ -$ 1,067.54$ 488.52$ 579.02$
59 7/1/2018 223,650.15$ 1,067.54$ -$ 1,067.54$ 489.78$ 577.76$
60 8/1/2018 223,160.37$ 1,067.54$ -$ 1,067.54$ 491.04$ 576.50$
61 9/1/2018 222,669.33$ 1,067.54$ -$ 1,067.54$ 492.31$ 575.23$ 62 10/1/2018 222,177.01$ 1,067.54$ -$ 1,067.54$ 493.58$ 573.96$
63 11/1/2018 221,683.43$ 1,067.54$ -$ 1,067.54$ 494.86$ 572.68$
64 12/1/2018 221,188.57$ 1,067.54$ -$ 1,067.54$ 496.14$ 571.40$
65 1/1/2019 220,692.43$ 1,067.54$ -$ 1,067.54$ 497.42$ 570.12$
66 2/1/2019 220,195.02$ 1,067.54$ -$ 1,067.54$ 498.70$ 568.84$
67 3/1/2019 219,696.31$ 1,067.54$ -$ 1,067.54$ 499.99$ 567.55$
68 4/1/2019 219,196.32$ 1,067.54$ -$ 1,067.54$ 501.28$ 566.26$
69 5/1/2019 218,695.04$ 1,067.54$ -$ 1,067.54$ 502.58$ 564.96$
70 6/1/2019 218,192.46$ 1,067.54$ -$ 1,067.54$ 503.88$ 563.66$
71 7/1/2019 217,688.58$ 1,067.54$ -$ 1,067.54$ 505.18$ 562.36$
72 8/1/2019 217,183.40$ 1,067.54$ -$ 1,067.54$ 506.48$ 561.06$
73 9/1/2019 216,676.92$ 1,067.54$ -$ 1,067.54$ 507.79$ 559.75$
74 10/1/2019 216,169.12$ 1,067.54$ -$ 1,067.54$ 509.10$ 558.44$
75 11/1/2019 215,660.02$ 1,067.54$ -$ 1,067.54$ 510.42$ 557.12$
76 12/1/2019 215,149.60$ 1,067.54$ -$ 1,067.54$ 511.74$ 555.80$ 77 1/1/2020 214,637.86$ 1,067.54$ -$ 1,067.54$ 513.06$ 554.48$
78 2/1/2020 214,124.80$ 1,067.54$ -$ 1,067.54$ 514.39$ 553.16$
79 3/1/2020 213,610.42$ 1,067.54$ -$ 1,067.54$ 515.71$ 551.83$
80 4/1/2020 213,094.70$ 1,067.54$ -$ 1,067.54$ 517.05$ 550.49$
81 5/1/2020 212,577.66$ 1,067.54$ -$ 1,067.54$ 518.38$ 549.16$
82 6/1/2020 212,059.28$ 1,067.54$ -$ 1,067.54$ 519.72$ 547.82$
83 7/1/2020 211,539.55$ 1,067.54$ -$ 1,067.54$ 521.06$ 546.48$
84 8/1/2020 211,018.49$ 1,067.54$ -$ 1,067.54$ 522.41$ 545.13$
85 9/1/2020 210,496.08$ 1,067.54$ -$ 1,067.54$ 523.76$ 543.78$
86 10/1/2020 209,972.32$ 1,067.54$ -$ 1,067.54$ 525.11$ 542.43$
87 11/1/2020 209,447.21$ 1,067.54$ -$ 1,067.54$ 526.47$ 541.07$
88 12/1/2020 208,920.74$ 1,067.54$ -$ 1,067.54$ 527.83$ 539.71$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
89 1/1/2021 208,392.91$ 1,067.54$ -$ 1,067.54$ 529.19$ 538.35$
90 2/1/2021 207,863.72$ 1,067.54$ -$ 1,067.54$ 530.56$ 536.98$
91 3/1/2021 207,333.16$ 1,067.54$ -$ 1,067.54$ 531.93$ 535.61$
92 4/1/2021 206,801.23$ 1,067.54$ -$ 1,067.54$ 533.30$ 534.24$
93 5/1/2021 206,267.92$ 1,067.54$ -$ 1,067.54$ 534.68$ 532.86$
94 6/1/2021 205,733.24$ 1,067.54$ -$ 1,067.54$ 536.06$ 531.48$
95 7/1/2021 205,197.18$ 1,067.54$ -$ 1,067.54$ 537.45$ 530.09$
96 8/1/2021 204,659.73$ 1,067.54$ -$ 1,067.54$ 538.84$ 528.70$
97 9/1/2021 204,120.89$ 1,067.54$ -$ 1,067.54$ 540.23$ 527.31$ 98 10/1/2021 203,580.66$ 1,067.54$ -$ 1,067.54$ 541.62$ 525.92$
99 11/1/2021 203,039.04$ 1,067.54$ -$ 1,067.54$ 543.02$ 524.52$
100 12/1/2021 202,496.02$ 1,067.54$ -$ 1,067.54$ 544.43$ 523.11$
101 1/1/2022 201,951.59$ 1,067.54$ -$ 1,067.54$ 545.83$ 521.71$
102 2/1/2022 201,405.76$ 1,067.54$ -$ 1,067.54$ 547.24$ 520.30$
103 3/1/2022 200,858.51$ 1,067.54$ -$ 1,067.54$ 548.66$ 518.88$
104 4/1/2022 200,309.86$ 1,067.54$ -$ 1,067.54$ 550.07$ 517.47$
105 5/1/2022 199,759.78$ 1,067.54$ -$ 1,067.54$ 551.49$ 516.05$
106 6/1/2022 199,208.29$ 1,067.54$ -$ 1,067.54$ 552.92$ 514.62$
107 7/1/2022 198,655.37$ 1,067.54$ -$ 1,067.54$ 554.35$ 513.19$
108 8/1/2022 198,101.02$ 1,067.54$ -$ 1,067.54$ 555.78$ 511.76$
109 9/1/2022 197,545.24$ 1,067.54$ -$ 1,067.54$ 557.22$ 510.33$
110 10/1/2022 196,988.03$ 1,067.54$ -$ 1,067.54$ 558.66$ 508.89$
111 11/1/2022 196,429.37$ 1,067.54$ -$ 1,067.54$ 560.10$ 507.44$
112 12/1/2022 195,869.27$ 1,067.54$ -$ 1,067.54$ 561.55$ 506.00$ 113 1/1/2023 195,307.73$ 1,067.54$ -$ 1,067.54$ 563.00$ 504.54$
114 2/1/2023 194,744.73$ 1,067.54$ -$ 1,067.54$ 564.45$ 503.09$
115 3/1/2023 194,180.28$ 1,067.54$ -$ 1,067.54$ 565.91$ 501.63$
116 4/1/2023 193,614.37$ 1,067.54$ -$ 1,067.54$ 567.37$ 500.17$
117 5/1/2023 193,047.00$ 1,067.54$ -$ 1,067.54$ 568.84$ 498.70$
118 6/1/2023 192,478.16$ 1,067.54$ -$ 1,067.54$ 570.31$ 497.24$
119 7/1/2023 191,907.86$ 1,067.54$ -$ 1,067.54$ 571.78$ 495.76$
120 8/1/2023 191,336.08$ 1,067.54$ -$ 1,067.54$ 573.26$ 494.28$
121 9/1/2023 190,762.82$ 1,067.54$ -$ 1,067.54$ 574.74$ 492.80$
122 10/1/2023 190,188.09$ 1,067.54$ -$ 1,067.54$ 576.22$ 491.32$
123 11/1/2023 189,611.87$ 1,067.54$ -$ 1,067.54$ 577.71$ 489.83$
124 12/1/2023 189,034.15$ 1,067.54$ -$ 1,067.54$ 579.20$ 488.34$
125 1/1/2024 188,454.95$ 1,067.54$ -$ 1,067.54$ 580.70$ 486.84$
126 2/1/2024 187,874.25$ 1,067.54$ -$ 1,067.54$ 582.20$ 485.34$
127 3/1/2024 187,292.05$ 1,067.54$ -$ 1,067.54$ 583.70$ 483.84$ 128 4/1/2024 186,708.35$ 1,067.54$ -$ 1,067.54$ 585.21$ 482.33$
129 5/1/2024 186,123.14$ 1,067.54$ -$ 1,067.54$ 586.72$ 480.82$
130 6/1/2024 185,536.42$ 1,067.54$ -$ 1,067.54$ 588.24$ 479.30$
131 7/1/2024 184,948.18$ 1,067.54$ -$ 1,067.54$ 589.76$ 477.78$
132 8/1/2024 184,358.42$ 1,067.54$ -$ 1,067.54$ 591.28$ 476.26$
133 9/1/2024 183,767.14$ 1,067.54$ -$ 1,067.54$ 592.81$ 474.73$
134 10/1/2024 183,174.33$ 1,067.54$ -$ 1,067.54$ 594.34$ 473.20$
135 11/1/2024 182,579.99$ 1,067.54$ -$ 1,067.54$ 595.88$ 471.66$
136 12/1/2024 181,984.11$ 1,067.54$ -$ 1,067.54$ 597.42$ 470.13$
137 1/1/2025 181,386.70$ 1,067.54$ -$ 1,067.54$ 598.96$ 468.58$
138 2/1/2025 180,787.74$ 1,067.54$ -$ 1,067.54$ 600.51$ 467.03$
139 3/1/2025 180,187.23$ 1,067.54$ -$ 1,067.54$ 602.06$ 465.48$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
140 4/1/2025 179,585.17$ 1,067.54$ -$ 1,067.54$ 603.61$ 463.93$
141 5/1/2025 178,981.56$ 1,067.54$ -$ 1,067.54$ 605.17$ 462.37$
142 6/1/2025 178,376.39$ 1,067.54$ -$ 1,067.54$ 606.74$ 460.81$
143 7/1/2025 177,769.65$ 1,067.54$ -$ 1,067.54$ 608.30$ 459.24$
144 8/1/2025 177,161.35$ 1,067.54$ -$ 1,067.54$ 609.87$ 457.67$
145 9/1/2025 176,551.48$ 1,067.54$ -$ 1,067.54$ 611.45$ 456.09$
146 10/1/2025 175,940.03$ 1,067.54$ -$ 1,067.54$ 613.03$ 454.51$
147 11/1/2025 175,327.00$ 1,067.54$ -$ 1,067.54$ 614.61$ 452.93$
148 12/1/2025 174,712.39$ 1,067.54$ -$ 1,067.54$ 616.20$ 451.34$ 149 1/1/2026 174,096.19$ 1,067.54$ -$ 1,067.54$ 617.79$ 449.75$
150 2/1/2026 173,478.39$ 1,067.54$ -$ 1,067.54$ 619.39$ 448.15$
151 3/1/2026 172,859.00$ 1,067.54$ -$ 1,067.54$ 620.99$ 446.55$
152 4/1/2026 172,238.02$ 1,067.54$ -$ 1,067.54$ 622.59$ 444.95$
153 5/1/2026 171,615.42$ 1,067.54$ -$ 1,067.54$ 624.20$ 443.34$
154 6/1/2026 170,991.22$ 1,067.54$ -$ 1,067.54$ 625.81$ 441.73$
155 7/1/2026 170,365.41$ 1,067.54$ -$ 1,067.54$ 627.43$ 440.11$
156 8/1/2026 169,737.98$ 1,067.54$ -$ 1,067.54$ 629.05$ 438.49$
157 9/1/2026 169,108.93$ 1,067.54$ -$ 1,067.54$ 630.68$ 436.86$
158 10/1/2026 168,478.25$ 1,067.54$ -$ 1,067.54$ 632.31$ 435.24$
159 11/1/2026 167,845.95$ 1,067.54$ -$ 1,067.54$ 633.94$ 433.60$
160 12/1/2026 167,212.01$ 1,067.54$ -$ 1,067.54$ 635.58$ 431.96$
161 1/1/2027 166,576.43$ 1,067.54$ -$ 1,067.54$ 637.22$ 430.32$
162 2/1/2027 165,939.21$ 1,067.54$ -$ 1,067.54$ 638.86$ 428.68$
163 3/1/2027 165,300.35$ 1,067.54$ -$ 1,067.54$ 640.52$ 427.03$ 164 4/1/2027 164,659.83$ 1,067.54$ -$ 1,067.54$ 642.17$ 425.37$
165 5/1/2027 164,017.66$ 1,067.54$ -$ 1,067.54$ 643.83$ 423.71$
166 6/1/2027 163,373.83$ 1,067.54$ -$ 1,067.54$ 645.49$ 422.05$
167 7/1/2027 162,728.34$ 1,067.54$ -$ 1,067.54$ 647.16$ 420.38$
168 8/1/2027 162,081.18$ 1,067.54$ -$ 1,067.54$ 648.83$ 418.71$
169 9/1/2027 161,432.35$ 1,067.54$ -$ 1,067.54$ 650.51$ 417.03$
170 10/1/2027 160,781.84$ 1,067.54$ -$ 1,067.54$ 652.19$ 415.35$
171 11/1/2027 160,129.65$ 1,067.54$ -$ 1,067.54$ 653.87$ 413.67$
172 12/1/2027 159,475.78$ 1,067.54$ -$ 1,067.54$ 655.56$ 411.98$
173 1/1/2028 158,820.22$ 1,067.54$ -$ 1,067.54$ 657.26$ 410.29$
174 2/1/2028 158,162.96$ 1,067.54$ -$ 1,067.54$ 658.95$ 408.59$
175 3/1/2028 157,504.01$ 1,067.54$ -$ 1,067.54$ 660.66$ 406.89$
176 4/1/2028 156,843.36$ 1,067.54$ -$ 1,067.54$ 662.36$ 405.18$
177 5/1/2028 156,180.99$ 1,067.54$ -$ 1,067.54$ 664.07$ 403.47$
178 6/1/2028 155,516.92$ 1,067.54$ -$ 1,067.54$ 665.79$ 401.75$ 179 7/1/2028 154,851.13$ 1,067.54$ -$ 1,067.54$ 667.51$ 400.03$
180 8/1/2028 154,183.62$ 1,067.54$ -$ 1,067.54$ 669.23$ 398.31$
181 9/1/2028 153,514.39$ 1,067.54$ -$ 1,067.54$ 670.96$ 396.58$
182 10/1/2028 152,843.43$ 1,067.54$ -$ 1,067.54$ 672.70$ 394.85$
183 11/1/2028 152,170.73$ 1,067.54$ -$ 1,067.54$ 674.43$ 393.11$
184 12/1/2028 151,496.30$ 1,067.54$ -$ 1,067.54$ 676.18$ 391.37$
185 1/1/2029 150,820.12$ 1,067.54$ -$ 1,067.54$ 677.92$ 389.62$
186 2/1/2029 150,142.20$ 1,067.54$ -$ 1,067.54$ 679.67$ 387.87$
187 3/1/2029 149,462.53$ 1,067.54$ -$ 1,067.54$ 681.43$ 386.11$
188 4/1/2029 148,781.10$ 1,067.54$ -$ 1,067.54$ 683.19$ 384.35$
189 5/1/2029 148,097.91$ 1,067.54$ -$ 1,067.54$ 684.95$ 382.59$
190 6/1/2029 147,412.95$ 1,067.54$ -$ 1,067.54$ 686.72$ 380.82$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
191 7/1/2029 146,726.23$ 1,067.54$ -$ 1,067.54$ 688.50$ 379.04$
192 8/1/2029 146,037.73$ 1,067.54$ -$ 1,067.54$ 690.28$ 377.26$
193 9/1/2029 145,347.45$ 1,067.54$ -$ 1,067.54$ 692.06$ 375.48$
194 10/1/2029 144,655.39$ 1,067.54$ -$ 1,067.54$ 693.85$ 373.69$
195 11/1/2029 143,961.54$ 1,067.54$ -$ 1,067.54$ 695.64$ 371.90$
196 12/1/2029 143,265.90$ 1,067.54$ -$ 1,067.54$ 697.44$ 370.10$
197 1/1/2030 142,568.47$ 1,067.54$ -$ 1,067.54$ 699.24$ 368.30$
198 2/1/2030 141,869.23$ 1,067.54$ -$ 1,067.54$ 701.05$ 366.50$
199 3/1/2030 141,168.18$ 1,067.54$ -$ 1,067.54$ 702.86$ 364.68$ 200 4/1/2030 140,465.33$ 1,067.54$ -$ 1,067.54$ 704.67$ 362.87$
201 5/1/2030 139,760.65$ 1,067.54$ -$ 1,067.54$ 706.49$ 361.05$
202 6/1/2030 139,054.16$ 1,067.54$ -$ 1,067.54$ 708.32$ 359.22$
203 7/1/2030 138,345.84$ 1,067.54$ -$ 1,067.54$ 710.15$ 357.39$
204 8/1/2030 137,635.70$ 1,067.54$ -$ 1,067.54$ 711.98$ 355.56$
205 9/1/2030 136,923.71$ 1,067.54$ -$ 1,067.54$ 713.82$ 353.72$
206 10/1/2030 136,209.89$ 1,067.54$ -$ 1,067.54$ 715.67$ 351.88$
207 11/1/2030 135,494.23$ 1,067.54$ -$ 1,067.54$ 717.51$ 350.03$
208 12/1/2030 134,776.71$ 1,067.54$ -$ 1,067.54$ 719.37$ 348.17$
209 1/1/2031 134,057.34$ 1,067.54$ -$ 1,067.54$ 721.23$ 346.31$
210 2/1/2031 133,336.12$ 1,067.54$ -$ 1,067.54$ 723.09$ 344.45$
211 3/1/2031 132,613.03$ 1,067.54$ -$ 1,067.54$ 724.96$ 342.58$
212 4/1/2031 131,888.07$ 1,067.54$ -$ 1,067.54$ 726.83$ 340.71$
213 5/1/2031 131,161.24$ 1,067.54$ -$ 1,067.54$ 728.71$ 338.83$
214 6/1/2031 130,432.53$ 1,067.54$ -$ 1,067.54$ 730.59$ 336.95$ 215 7/1/2031 129,701.94$ 1,067.54$ -$ 1,067.54$ 732.48$ 335.06$
216 8/1/2031 128,969.47$ 1,067.54$ -$ 1,067.54$ 734.37$ 333.17$
217 9/1/2031 128,235.10$ 1,067.54$ -$ 1,067.54$ 736.27$ 331.27$
218 10/1/2031 127,498.83$ 1,067.54$ -$ 1,067.54$ 738.17$ 329.37$
219 11/1/2031 126,760.66$ 1,067.54$ -$ 1,067.54$ 740.08$ 327.47$
220 12/1/2031 126,020.58$ 1,067.54$ -$ 1,067.54$ 741.99$ 325.55$
221 1/1/2032 125,278.60$ 1,067.54$ -$ 1,067.54$ 743.90$ 323.64$
222 2/1/2032 124,534.69$ 1,067.54$ -$ 1,067.54$ 745.83$ 321.71$
223 3/1/2032 123,788.87$ 1,067.54$ -$ 1,067.54$ 747.75$ 319.79$
224 4/1/2032 123,041.11$ 1,067.54$ -$ 1,067.54$ 749.68$ 317.86$
225 5/1/2032 122,291.43$ 1,067.54$ -$ 1,067.54$ 751.62$ 315.92$
226 6/1/2032 121,539.81$ 1,067.54$ -$ 1,067.54$ 753.56$ 313.98$
227 7/1/2032 120,786.24$ 1,067.54$ -$ 1,067.54$ 755.51$ 312.03$
228 8/1/2032 120,030.73$ 1,067.54$ -$ 1,067.54$ 757.46$ 310.08$
229 9/1/2032 119,273.27$ 1,067.54$ -$ 1,067.54$ 759.42$ 308.12$ 230 10/1/2032 118,513.85$ 1,067.54$ -$ 1,067.54$ 761.38$ 306.16$
231 11/1/2032 117,752.47$ 1,067.54$ -$ 1,067.54$ 763.35$ 304.19$
232 12/1/2032 116,989.13$ 1,067.54$ -$ 1,067.54$ 765.32$ 302.22$
233 1/1/2033 116,223.81$ 1,067.54$ -$ 1,067.54$ 767.30$ 300.24$
234 2/1/2033 115,456.51$ 1,067.54$ -$ 1,067.54$ 769.28$ 298.26$
235 3/1/2033 114,687.23$ 1,067.54$ -$ 1,067.54$ 771.27$ 296.28$
236 4/1/2033 113,915.97$ 1,067.54$ -$ 1,067.54$ 773.26$ 294.28$
237 5/1/2033 113,142.71$ 1,067.54$ -$ 1,067.54$ 775.26$ 292.29$
238 6/1/2033 112,367.45$ 1,067.54$ -$ 1,067.54$ 777.26$ 290.28$
239 7/1/2033 111,590.19$ 1,067.54$ -$ 1,067.54$ 779.27$ 288.27$
240 8/1/2033 110,810.93$ 1,067.54$ -$ 1,067.54$ 781.28$ 286.26$
241 9/1/2033 110,029.65$ 1,067.54$ -$ 1,067.54$ 783.30$ 284.24$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
242 10/1/2033 109,246.35$ 1,067.54$ -$ 1,067.54$ 785.32$ 282.22$
243 11/1/2033 108,461.03$ 1,067.54$ -$ 1,067.54$ 787.35$ 280.19$
244 12/1/2033 107,673.68$ 1,067.54$ -$ 1,067.54$ 789.38$ 278.16$
245 1/1/2034 106,884.30$ 1,067.54$ -$ 1,067.54$ 791.42$ 276.12$
246 2/1/2034 106,092.87$ 1,067.54$ -$ 1,067.54$ 793.47$ 274.07$
247 3/1/2034 105,299.40$ 1,067.54$ -$ 1,067.54$ 795.52$ 272.02$
248 4/1/2034 104,503.89$ 1,067.54$ -$ 1,067.54$ 797.57$ 269.97$
249 5/1/2034 103,706.31$ 1,067.54$ -$ 1,067.54$ 799.63$ 267.91$
250 6/1/2034 102,906.68$ 1,067.54$ -$ 1,067.54$ 801.70$ 265.84$ 251 7/1/2034 102,104.98$ 1,067.54$ -$ 1,067.54$ 803.77$ 263.77$
252 8/1/2034 101,301.21$ 1,067.54$ -$ 1,067.54$ 805.85$ 261.69$
253 9/1/2034 100,495.37$ 1,067.54$ -$ 1,067.54$ 807.93$ 259.61$
254 10/1/2034 99,687.44$ 1,067.54$ -$ 1,067.54$ 810.02$ 257.53$
255 11/1/2034 98,877.42$ 1,067.54$ -$ 1,067.54$ 812.11$ 255.43$
256 12/1/2034 98,065.32$ 1,067.54$ -$ 1,067.54$ 814.21$ 253.34$
257 1/1/2035 97,251.11$ 1,067.54$ -$ 1,067.54$ 816.31$ 251.23$
258 2/1/2035 96,434.80$ 1,067.54$ -$ 1,067.54$ 818.42$ 249.12$
259 3/1/2035 95,616.38$ 1,067.54$ -$ 1,067.54$ 820.53$ 247.01$
260 4/1/2035 94,795.85$ 1,067.54$ -$ 1,067.54$ 822.65$ 244.89$
261 5/1/2035 93,973.20$ 1,067.54$ -$ 1,067.54$ 824.78$ 242.76$
262 6/1/2035 93,148.42$ 1,067.54$ -$ 1,067.54$ 826.91$ 240.63$
263 7/1/2035 92,321.52$ 1,067.54$ -$ 1,067.54$ 829.04$ 238.50$
264 8/1/2035 91,492.47$ 1,067.54$ -$ 1,067.54$ 831.19$ 236.36$
265 9/1/2035 90,661.29$ 1,067.54$ -$ 1,067.54$ 833.33$ 234.21$ 266 10/1/2035 89,827.95$ 1,067.54$ -$ 1,067.54$ 835.49$ 232.06$
267 11/1/2035 88,992.47$ 1,067.54$ -$ 1,067.54$ 837.64$ 229.90$
268 12/1/2035 88,154.82$ 1,067.54$ -$ 1,067.54$ 839.81$ 227.73$
269 1/1/2036 87,315.02$ 1,067.54$ -$ 1,067.54$ 841.98$ 225.56$
270 2/1/2036 86,473.04$ 1,067.54$ -$ 1,067.54$ 844.15$ 223.39$
271 3/1/2036 85,628.89$ 1,067.54$ -$ 1,067.54$ 846.33$ 221.21$
272 4/1/2036 84,782.55$ 1,067.54$ -$ 1,067.54$ 848.52$ 219.02$
273 5/1/2036 83,934.03$ 1,067.54$ -$ 1,067.54$ 850.71$ 216.83$
274 6/1/2036 83,083.32$ 1,067.54$ -$ 1,067.54$ 852.91$ 214.63$
275 7/1/2036 82,230.41$ 1,067.54$ -$ 1,067.54$ 855.11$ 212.43$
276 8/1/2036 81,375.30$ 1,067.54$ -$ 1,067.54$ 857.32$ 210.22$
277 9/1/2036 80,517.98$ 1,067.54$ -$ 1,067.54$ 859.54$ 208.00$
278 10/1/2036 79,658.44$ 1,067.54$ -$ 1,067.54$ 861.76$ 205.78$
279 11/1/2036 78,796.69$ 1,067.54$ -$ 1,067.54$ 863.98$ 203.56$
280 12/1/2036 77,932.70$ 1,067.54$ -$ 1,067.54$ 866.21$ 201.33$ 281 1/1/2037 77,066.49$ 1,067.54$ -$ 1,067.54$ 868.45$ 199.09$
282 2/1/2037 76,198.04$ 1,067.54$ -$ 1,067.54$ 870.70$ 196.84$
283 3/1/2037 75,327.34$ 1,067.54$ -$ 1,067.54$ 872.95$ 194.60$
284 4/1/2037 74,454.40$ 1,067.54$ -$ 1,067.54$ 875.20$ 192.34$
285 5/1/2037 73,579.20$ 1,067.54$ -$ 1,067.54$ 877.46$ 190.08$
286 6/1/2037 72,701.73$ 1,067.54$ -$ 1,067.54$ 879.73$ 187.81$
287 7/1/2037 71,822.01$ 1,067.54$ -$ 1,067.54$ 882.00$ 185.54$
288 8/1/2037 70,940.00$ 1,067.54$ -$ 1,067.54$ 884.28$ 183.26$
289 9/1/2037 70,055.73$ 1,067.54$ -$ 1,067.54$ 886.56$ 180.98$
290 10/1/2037 69,169.16$ 1,067.54$ -$ 1,067.54$ 888.85$ 178.69$
291 11/1/2037 68,280.31$ 1,067.54$ -$ 1,067.54$ 891.15$ 176.39$
292 12/1/2037 67,389.16$ 1,067.54$ -$ 1,067.54$ 893.45$ 174.09$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
293 1/1/2038 66,495.71$ 1,067.54$ -$ 1,067.54$ 895.76$ 171.78$
294 2/1/2038 65,599.94$ 1,067.54$ -$ 1,067.54$ 898.07$ 169.47$
295 3/1/2038 64,701.87$ 1,067.54$ -$ 1,067.54$ 900.39$ 167.15$
296 4/1/2038 63,801.48$ 1,067.54$ -$ 1,067.54$ 902.72$ 164.82$
297 5/1/2038 62,898.76$ 1,067.54$ -$ 1,067.54$ 905.05$ 162.49$
298 6/1/2038 61,993.70$ 1,067.54$ -$ 1,067.54$ 907.39$ 160.15$
299 7/1/2038 61,086.31$ 1,067.54$ -$ 1,067.54$ 909.73$ 157.81$
300 8/1/2038 60,176.58$ 1,067.54$ -$ 1,067.54$ 912.08$ 155.46$
301 9/1/2038 59,264.49$ 1,067.54$ -$ 1,067.54$ 914.44$ 153.10$ 302 10/1/2038 58,350.05$ 1,067.54$ -$ 1,067.54$ 916.80$ 150.74$
303 11/1/2038 57,433.25$ 1,067.54$ -$ 1,067.54$ 919.17$ 148.37$
304 12/1/2038 56,514.08$ 1,067.54$ -$ 1,067.54$ 921.55$ 145.99$
305 1/1/2039 55,592.53$ 1,067.54$ -$ 1,067.54$ 923.93$ 143.61$
306 2/1/2039 54,668.60$ 1,067.54$ -$ 1,067.54$ 926.31$ 141.23$
307 3/1/2039 53,742.29$ 1,067.54$ -$ 1,067.54$ 928.71$ 138.83$
308 4/1/2039 52,813.58$ 1,067.54$ -$ 1,067.54$ 931.11$ 136.44$
309 5/1/2039 51,882.48$ 1,067.54$ -$ 1,067.54$ 933.51$ 134.03$
310 6/1/2039 50,948.97$ 1,067.54$ -$ 1,067.54$ 935.92$ 131.62$
311 7/1/2039 50,013.04$ 1,067.54$ -$ 1,067.54$ 938.34$ 129.20$
312 8/1/2039 49,074.70$ 1,067.54$ -$ 1,067.54$ 940.76$ 126.78$
313 9/1/2039 48,133.94$ 1,067.54$ -$ 1,067.54$ 943.19$ 124.35$
314 10/1/2039 47,190.74$ 1,067.54$ -$ 1,067.54$ 945.63$ 121.91$
315 11/1/2039 46,245.11$ 1,067.54$ -$ 1,067.54$ 948.07$ 119.47$
316 12/1/2039 45,297.04$ 1,067.54$ -$ 1,067.54$ 950.52$ 117.02$ 317 1/1/2040 44,346.51$ 1,067.54$ -$ 1,067.54$ 952.98$ 114.56$
318 2/1/2040 43,393.53$ 1,067.54$ -$ 1,067.54$ 955.44$ 112.10$
319 3/1/2040 42,438.09$ 1,067.54$ -$ 1,067.54$ 957.91$ 109.63$
320 4/1/2040 41,480.18$ 1,067.54$ -$ 1,067.54$ 960.38$ 107.16$
321 5/1/2040 40,519.80$ 1,067.54$ -$ 1,067.54$ 962.86$ 104.68$
322 6/1/2040 39,556.93$ 1,067.54$ -$ 1,067.54$ 965.35$ 102.19$
323 7/1/2040 38,591.58$ 1,067.54$ -$ 1,067.54$ 967.85$ 99.69$
324 8/1/2040 37,623.74$ 1,067.54$ -$ 1,067.54$ 970.35$ 97.19$
325 9/1/2040 36,653.39$ 1,067.54$ -$ 1,067.54$ 972.85$ 94.69$
326 10/1/2040 35,680.54$ 1,067.54$ -$ 1,067.54$ 975.37$ 92.17$
327 11/1/2040 34,705.17$ 1,067.54$ -$ 1,067.54$ 977.89$ 89.66$
328 12/1/2040 33,727.28$ 1,067.54$ -$ 1,067.54$ 980.41$ 87.13$
329 1/1/2041 32,746.87$ 1,067.54$ -$ 1,067.54$ 982.94$ 84.60$
330 2/1/2041 31,763.93$ 1,067.54$ -$ 1,067.54$ 985.48$ 82.06$
331 3/1/2041 30,778.44$ 1,067.54$ -$ 1,067.54$ 988.03$ 79.51$ 332 4/1/2041 29,790.41$ 1,067.54$ -$ 1,067.54$ 990.58$ 76.96$
333 5/1/2041 28,799.83$ 1,067.54$ -$ 1,067.54$ 993.14$ 74.40$
334 6/1/2041 27,806.69$ 1,067.54$ -$ 1,067.54$ 995.71$ 71.83$
335 7/1/2041 26,810.98$ 1,067.54$ -$ 1,067.54$ 998.28$ 69.26$
336 8/1/2041 25,812.70$ 1,067.54$ -$ 1,067.54$ 1,000.86$ 66.68$
337 9/1/2041 24,811.84$ 1,067.54$ -$ 1,067.54$ 1,003.44$ 64.10$
338 10/1/2041 23,808.40$ 1,067.54$ -$ 1,067.54$ 1,006.04$ 61.51$
339 11/1/2041 22,802.36$ 1,067.54$ -$ 1,067.54$ 1,008.63$ 58.91$
340 12/1/2041 21,793.73$ 1,067.54$ -$ 1,067.54$ 1,011.24$ 56.30$
341 1/1/2042 20,782.49$ 1,067.54$ -$ 1,067.54$ 1,013.85$ 53.69$
342 2/1/2042 19,768.64$ 1,067.54$ -$ 1,067.54$ 1,016.47$ 51.07$
343 3/1/2042 18,752.16$ 1,067.54$ -$ 1,067.54$ 1,019.10$ 48.44$
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Pmt.
No.Payment Date Beginning Balance
Scheduled
PaymentExtra Payment Total Payment Principal Interest
344 4/1/2042 17,733.07$ 1,067.54$ -$ 1,067.54$ 1,021.73$ 45.81$
345 5/1/2042 16,711.34$ 1,067.54$ -$ 1,067.54$ 1,024.37$ 43.17$
346 6/1/2042 15,686.97$ 1,067.54$ -$ 1,067.54$ 1,027.02$ 40.52$
347 7/1/2042 14,659.95$ 1,067.54$ -$ 1,067.54$ 1,029.67$ 37.87$
348 8/1/2042 13,630.28$ 1,067.54$ -$ 1,067.54$ 1,032.33$ 35.21$
349 9/1/2042 12,597.95$ 1,067.54$ -$ 1,067.54$ 1,035.00$ 32.54$
350 10/1/2042 11,562.95$ 1,067.54$ -$ 1,067.54$ 1,037.67$ 29.87$
351 11/1/2042 10,525.28$ 1,067.54$ -$ 1,067.54$ 1,040.35$ 27.19$
352 12/1/2042 9,484.93$ 1,067.54$ -$ 1,067.54$ 1,043.04$ 24.50$ 353 1/1/2043 8,441.90$ 1,067.54$ -$ 1,067.54$ 1,045.73$ 21.81$
354 2/1/2043 7,396.16$ 1,067.54$ -$ 1,067.54$ 1,048.43$ 19.11$
355 3/1/2043 6,347.73$ 1,067.54$ -$ 1,067.54$ 1,051.14$ 16.40$
356 4/1/2043 5,296.59$ 1,067.54$ -$ 1,067.54$ 1,053.86$ 13.68$
357 5/1/2043 4,242.73$ 1,067.54$ -$ 1,067.54$ 1,056.58$ 10.96$
358 6/1/2043 3,186.15$ 1,067.54$ -$ 1,067.54$ 1,059.31$ 8.23$
359 7/1/2043 2,126.84$ 1,067.54$ -$ 1,067.54$ 1,062.05$ 5.49$
360 8/1/2043 1,064.79$ 1,067.54$ -$ 1,064.79$ 1,062.04$ 2.75$
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1,067.54$
360
360
-$
134,314.76$
Cumulative Interest
645.83$
1,290.58$
1,934.23$
2,576.79$
3,218.24$
3,858.60$
4,497.86$
5,136.01$
5,773.04$
6,408.97$ 7,043.78$
7,677.48$
8,310.05$
8,941.50$
9,571.82$
10,201.01$
10,829.08$
11,456.00$
12,081.79$
12,706.43$
13,329.94$
13,952.29$
14,573.50$
15,193.55$
15,812.44$
16,430.18$
17,046.76$
17,662.17$
18,276.41$
18,889.48$
19,501.37$
20,112.09$
20,721.63$
21,329.99$
21,937.16$
22,543.14$
23,147.93$
Loan summary
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Cumulative Interest
23,751.52$
24,353.92$
24,955.11$
25,555.10$
26,153.88$
26,751.45$
27,347.80$
27,942.94$
28,536.86$29,129.55$
29,721.02$
30,311.26$
30,900.26$
31,488.03$
32,074.56$
32,659.85$
33,243.89$
33,826.68$
34,408.22$
34,988.50$
35,567.53$
36,145.29$
36,721.79$
37,297.01$37,870.97$
38,443.65$
39,015.06$
39,585.18$
40,154.02$
40,721.57$
41,287.82$
41,852.79$
42,416.45$
42,978.81$
43,539.87$
44,099.62$
44,658.05$
45,215.18$
45,770.98$ 46,325.46$
46,878.62$
47,430.44$
47,980.94$
48,530.10$
49,077.92$
49,624.39$
50,169.52$
50,713.31$
51,255.73$
51,796.81$
52,336.52$
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Cumulative Interest
52,874.87$
53,411.85$
53,947.46$
54,481.70$
55,014.55$
55,546.03$
56,076.12$
56,604.83$
57,132.14$57,658.06$
58,182.58$
58,705.69$
59,227.40$
59,747.70$
60,266.58$
60,784.05$
61,300.09$
61,814.72$
62,327.91$
62,839.67$
63,349.99$
63,858.88$
64,366.32$
64,872.32$65,376.86$
65,879.95$
66,381.59$
66,881.76$
67,380.46$
67,877.70$
68,373.46$
68,867.74$
69,360.55$
69,851.87$
70,341.70$
70,830.04$
71,316.88$
71,802.22$
72,286.06$ 72,768.39$
73,249.21$
73,728.51$
74,206.29$
74,682.55$
75,157.28$
75,630.48$
76,102.15$
76,572.27$
77,040.85$
77,507.89$
77,973.37$
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Cumulative Interest
78,437.30$
78,899.67$
79,360.48$
79,819.71$
80,277.38$
80,733.47$
81,187.98$
81,640.91$
82,092.25$82,542.00$
82,990.15$
83,436.71$
83,881.65$
84,324.99$
84,766.72$
85,206.83$
85,645.32$
86,082.19$
86,517.42$
86,951.02$
87,382.99$
87,813.31$
88,241.99$
88,669.01$89,094.38$
89,518.10$
89,940.15$
90,360.53$
90,779.24$
91,196.27$
91,611.62$
92,025.29$
92,437.27$
92,847.56$
93,256.14$
93,663.03$
94,068.21$
94,471.68$
94,873.43$ 95,273.46$
95,671.77$
96,068.35$
96,463.19$
96,856.30$
97,247.67$
97,637.28$
98,025.15$
98,411.26$
98,795.61$
99,178.20$
99,559.02$
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Cumulative Interest
99,938.06$
100,315.32$
100,690.81$
101,064.50$
101,436.40$
101,806.50$
102,174.80$
102,541.30$
102,905.98$103,268.85$
103,629.90$
103,989.12$
104,346.52$
104,702.08$
105,055.80$
105,407.67$
105,757.70$
106,105.87$
106,452.19$
106,796.64$
107,139.22$
107,479.93$
107,818.77$
108,155.72$108,490.78$
108,823.95$
109,155.23$
109,484.60$
109,812.06$
110,137.62$
110,461.25$
110,782.97$
111,102.75$
111,420.61$
111,736.53$
112,050.51$
112,362.54$
112,672.62$
112,980.74$ 113,286.90$
113,591.10$
113,893.32$
114,193.56$
114,491.83$
114,788.10$
115,082.38$
115,374.67$
115,664.95$
115,953.23$
116,239.49$
116,523.73$
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Cumulative Interest
116,805.95$
117,086.14$
117,364.30$
117,640.42$
117,914.49$
118,186.51$
118,456.48$
118,724.39$
118,990.23$119,254.00$
119,515.70$
119,775.31$
120,032.84$
120,288.27$
120,541.61$
120,792.84$
121,041.96$
121,288.97$
121,533.86$
121,776.62$
122,017.26$
122,255.75$
122,492.11$
122,726.32$122,958.37$
123,188.27$
123,416.00$
123,641.57$
123,864.96$
124,086.16$
124,305.19$
124,522.02$
124,736.65$
124,949.08$
125,159.30$
125,367.30$
125,573.08$
125,776.64$
125,977.97$ 126,177.06$
126,373.90$
126,568.50$
126,760.84$
126,950.92$
127,138.73$
127,324.27$
127,507.53$
127,688.51$
127,867.20$
128,043.59$
128,217.68$
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Cumulative Interest
128,389.46$
128,558.92$
128,726.07$
128,890.89$
129,053.38$
129,213.53$
129,371.34$
129,526.79$
129,679.89$129,830.63$
129,979.00$
130,124.99$
130,268.61$
130,409.83$
130,548.67$
130,685.10$
130,819.13$
130,950.75$
131,079.95$
131,206.73$
131,331.07$
131,452.98$
131,572.45$
131,689.47$131,804.03$
131,916.13$
132,025.76$
132,132.92$
132,237.59$
132,339.78$
132,439.48$
132,536.67$
132,631.36$
132,723.54$
132,813.19$
132,900.32$
132,984.92$
133,066.97$
133,146.48$ 133,223.44$
133,297.84$
133,369.68$
133,438.94$
133,505.62$
133,569.72$
133,631.22$
133,690.13$
133,746.43$
133,800.12$
133,851.19$
133,899.63$
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Cumulative Interest
133,945.44$
133,988.61$
134,029.13$
134,067.01$
134,102.22$
134,134.76$
134,164.63$
134,191.82$
134,216.33$134,238.13$
134,257.24$
134,273.64$
134,287.32$
134,298.28$
134,306.51$
134,312.01$
134,314.76$
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Chapter 4 - Master it!
Years until retirement: 30
Amount to withdraw each year: 90,000$
Years to withdraw in retirement: 20$
Interest rate: 8%
a.
b.
c.
Employer's annual contribution: 1,500$
Years until trust fund distribution: 20
Amount of trust fund distribution: 25,000$
Suppose your friend's employer will contribute to the account each year as part of th
a family trust several years from now. What amount must she deposit annually now
Excel is a tool for solving problems, but with many time value of money problems, y
This is a classic retirement problem. A friend is celebrating her birthday and wants to
retirement and retirement spending goals:
Because your friend is planning ahead, the first withdrawal will not take place until o
for her retirement fund.
If she starts making these deposits in one year and makes her last deposit on the day
withdrawals at retirement?
Suppose your friend has just inherited a large sum of money. Rather than making eq
cover her retirement needs. What amount does she have to deposit today?
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e company's profit sharing plan. In addition, your friend expects a distribution from
to be able to make the desired withdrawals at retirement?
u may still need to draw a time line.
start saving for her anticipated retirement. She has the following years to
ne year after she retires. She wants to make equal annual deposits into her account
she retires, what amount must she deposit annually to be able to make the desired
al annual payments, she has decided to make one lump sum deposit today to
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Master it! Solution
Amount needed at retirement:
a.
Amount to save each year:
b.
Lump sum deposited today:
c.
Value of employer's contribution at retirement:
Value of trust fund at retirement:
Amount to save each year now:
In order to answer any of these questions, first we need to know how much your frie
each of the parts of the problem, we will solve for this amount now, which will be:
The amount your friend must save each year to fund her retirement is:
The lump sum your friend must deposit today to fund her retirement is:
To find the amount of the annual deposit now, it is easier to break down the compo
deposit, we get:
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nd will need when she is ready to retire. Since this amount will be the same for
ents of the problem. Doing so for each of the following to find your friend's annual