© 2004 McGraw-Hill Ryerson. McGraw-Hill Ryerson Chapter 16 Accounting for Income Taxes.
1111 McGraw-Hill Ryerson© 11-1 Chapter 11 O rdinary A nnuities McGraw-Hill Ryerson©
-
Upload
jonathan-goodman -
Category
Documents
-
view
231 -
download
2
Transcript of 1111 McGraw-Hill Ryerson© 11-1 Chapter 11 O rdinary A nnuities McGraw-Hill Ryerson©
11-111111111
McGraw-Hill Ryerson©
Chapter 11
OrdinaryOrdinaryAnnuitiesAnnuities
McGraw-Hill Ryerson©
11-211111111
McGraw-Hill Ryerson©
Calculate the…
Learning ObjectivesLearning ObjectivesAfter completing this chapter, you will be able to:
… number of payments in ordinary and deferred annuities
… payment size in ordinary and deferred annuities
… interest rate in ordinary annuities
LO-1LO-1
LO-2LO-2
LO-3LO-3
11-311111111
McGraw-Hill Ryerson©
Using your financial calculatorUsing your financial calculator
we need to reorganize the formulae to solve algebraically
… solve for payment number or size or interest rate using the
same steps as before …
11-411111111
McGraw-Hill Ryerson©
Finding the Payment Size….
PMT
11-511111111
McGraw-Hill Ryerson©
Your life partner somehow convinced you that you can’t afford the car of your dreams, priced at $28800. You are advised to… “Save up for 4 years and then buy the car for cash.” How much would you have to save each month, if you could invest with a return of
10% compounded monthly?
You need to decide if this situation involves… a PV or a FV and then use the appropriate formula...
PMT
As you have to save up the $28,800, i.e. in the future, FV = $28,800
Assume you have no savings … PV = 0
Finding Payment Size of an
Ordinary Simple Annuity
Finding Payment Size of an
Ordinary Simple Annuity
11-611111111
McGraw-Hill Ryerson©
Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4 years and then buy the car for cash.” How much
would you have to save each month, if you could invest with a return of
10% compounded monthly?
Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4 years and then buy the car for cash.” How much
would you have to save each month, if you could invest with a return of
10% compounded monthly?
Finding Payment Size of an
Ordinary Simple Annuity
Finding Payment Size of an
Ordinary Simple Annuity
48
12PMT = - 490.44
10 0
28800
Formula solution Formula solution
11-711111111
McGraw-Hill Ryerson©
[FV = PMT (1+ i)n - 1i ]i
PV = PMT 1-(1+ i)-n[ ]
Which Formula?Which Formula?
Algebraic Method of Solving for PMT Algebraic Method of Solving for PMT
(a) If the payments form a Simple Annuity go directly to 2. 1.1.
If the annuity’s PV is
known, substitute values of PV, n,
and i into PV formula.
If the annuity’s FV is known,
substitute values of FV, n, and i
into FV formula.
3.3. && 4.4.
(b) If the payments form a General Annuity, find c and i2
2.2.
11-811111111
McGraw-Hill Ryerson©
Calculate the quantity within the square brackets.
Rearrange the equation to solve for PMT.
i[FV = PMT (1+ i)n - 1] i
PV = PMT 1-(1+ i)-n[ ]
Which Formula?Which Formula?
Algebraic Method of Solving for PMT Algebraic Method of Solving for PMT
3.3.
4.4.
Applying Method… Applying Method…
11-911111111
McGraw-Hill Ryerson©
Finding Payment Size of an
Ordinary Simple Annuity
Finding Payment Size of an
Ordinary Simple Annuity
Which Formula?Which Formula? Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4
years and then buy the car for cash.”
How much would you have to save each month, if you could invest with a
return of 10% compounded monthly?
Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4
years and then buy the car for cash.”
How much would you have to save each month, if you could invest with a
return of 10% compounded monthly?
[FV = PMT (1+ i)n - 1i ]
As the annuity’s FV is known, therefore, the FV formula is used
2.2.
Extract necessary data...
FV = 28800 n = 4*12 = 48i = .10/12 c = 1 PMT = ?
PV = 0
11-1011111111
McGraw-Hill Ryerson©
12.10
28800
481
1
Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4
years and then buy the car for cash.”
How much would you have to save each month, if you could invest with a
return of 10% compounded monthly?
Your life partner somehow convinced you that you can’t afford the
car of your dreams, priced at $28800. (At least
not right now). You are advised to… “Save up for 4
years and then buy the car for cash.”
How much would you have to save each month, if you could invest with a
return of 10% compounded monthly?
0.00831.0083 1.48940.48940.008358.7225490.44
[FV = PMT (1+ i)n - 1i ]FormulaFormula
FV = 28800 n = 4*12 = 48i = .10/12 c = 1 PMT = ?
PV = 0
…another example…another example
11-1111111111
McGraw-Hill Ryerson©
The The
11-1211111111
McGraw-Hill Ryerson©
Your parents are discussing the terms of the $100 000 mortgage that they have offered to
hold in the purchase of your first home. They are considering an interest rate of 5% compounded monthly. If you were to take 20 years to
repay the mortgage, find the size of the
monthly payment.
Your parents are discussing the terms of the $100 000 mortgage that they have offered to
hold in the purchase of your first home. They are considering an interest rate of 5% compounded monthly. If you were to take 20 years to
repay the mortgage, find the size of the
monthly payment.
2405
0
100 000
PMT = -659.9612
n =12*20 = 240PV = $100000
FV = 0
Formula solutionFormula solution
11-1311111111
McGraw-Hill Ryerson©
Your parents are
discussing the terms of the 100 000 mortgage
that they have offered to hold in the purchase of your first home. They
are considering an interest rate of 5%
compounded monthly. If you were to take 20
years to repay the mortgage, find the size
of the monthly payment..
Your parents are
discussing the terms of the 100 000 mortgage
that they have offered to hold in the purchase of your first home. They
are considering an interest rate of 5%
compounded monthly. If you were to take 20
years to repay the mortgage, find the size
of the monthly payment..
i = .05/12
Extract necessary data...
n =12*20 = 240
PV = $100000
FV = 0C =1
11-1411111111
McGraw-Hill Ryerson©
Choose appropriate formula and Solve
As the annuity’s PV is known, the PV formula is used2.2.
i = .05/12n =12*20 =240 PV = $100000i
PV = PMT 1-(1+ i)-n[ ]FormulaFormula
12.05 1
100 000
240 1
0.00421.0042 0.3686-0.6314151.530.0015659.96Size of monthly
mortgage payment
Size of monthly mortgage
payment
11-1511111111
McGraw-Hill Ryerson©
Amount$
How much interest will you pay your parents over the 20 year period?
Monthly Payment Number of Payments659.96 240 158,390.40
Amount Borrowed 100,000.00
Total Interest Paid 58,390.40
x
11-1611111111
McGraw-Hill Ryerson©
PMT = -700
As this amount of interest
shocks you, you discuss the
possibility of making payments
of $700/month, to save some time
and interest costs.
Determine the time
it will take you to repay your
mortgage at this new
rate.
700
N = 217.52
Formula solutionFormula solution
218 payments = 18 yrs 2months218 payments = 18 yrs 2months
11-1711111111
McGraw-Hill Ryerson©
FormulaFormula iPMTPV i
1ln
1ln[ ]n
0.0042
i = .05/12 PMT = $700PV = $100,000 C = 1 n 0
12.05 1
700
100 000
1
1.0042 0.00420.5952-0.4048-0.9045-217.52 217.52
218 payments = 18 yrs 2months218 payments = 18 yrs 2months
11-1811111111
McGraw-Hill Ryerson©
1. Base formulai
-ni)PMTPV
(11[ ]2. To isolate n, divide both
sides by PMTPMTPMT
…Continue……Continue…
Developing the FormulaFormula
PMTPV
i-ni)(11[ ]
i
-ni)PMTPV
(11 ][
FormulaFormula iPMT
PV i*
1ln
1ln[ ]n
11-1911111111
McGraw-Hill Ryerson©
(a) Multiply both sides by i
3. Continue to isolate n.
PMTPV
i-ni)(11[ ]
PMTPV -ni)(11
i[ ] *i *i
(b) Reorganize equation
(c) Now Take the natural logarithm (ln or lnx) of both sides
-n* ln
PMT *iPV -n1 i)(1
-ni)(1
i) (1 ln
(d) Solving for n… divide both sides by
ln(1+i) ln(1+i) ln(1+i)
…from 2.
PMT
*iPV1
[ ]PMT*iPV1
-n* ln i)(1 ln[ ]PMT*iPV1
PMTPV*i
i1ln
1lnn
[ ]
11-2011111111
McGraw-Hill Ryerson©
700.00 217.52 152,264.00
Total Interest Saved 6,126.40
Approximately how much money do you save in interest charges by paying $700/month,
rather than $659.91/month?
Amount$
Monthly Payment Number of Paymentsx158,390.4
0659.96 240
11-2111111111
McGraw-Hill Ryerson©
If you could see your way to a further increase
of $25/month, (a) how much
faster would you pay off the
mortgage, and (b) approximately
how much less interest would be
involved?
725
PMT = -725N = 205.62
Paying $725 206 payments = 17 yrs
2months
Paying $725 206 payments = 17 yrs
2months
Formula solutionFormula solution
11-2211111111
McGraw-Hill Ryerson©
i = .05/12 PMT = $725PV = $100,000 C = 1 n 0
0.0042
12.05 1
725
100 000
1
1.0042 0.00420.5747-0.4253-0.8550-205.52
206 payments = 17 yrs 2months206 payments = 17 yrs 2months
205.52
FormulaFormula iPMT
PV i*
1ln
1ln[ ]n
11-2311111111
McGraw-Hill Ryerson©
(b)Total Interest Saved 3,189.50
700.00 217.52 or 218 152,264.00
Amount$
Monthly Payment Number of Paymentsx
725.00 205.62 or 206 149,074.50(a) Payments Saved 12
11-2411111111
McGraw-Hill Ryerson©
11-2511111111
McGraw-Hill Ryerson©
York Furniture has a promotion on a bedroom set selling for $2250. Buyers will pay “no money down and no payments for 12 months.”
The first of 24 equal monthly payments is due 12 months from the purchase date. What should the monthly payments be if York Furniture earns 10% compounded monthly on its account receivable during both the deferral period
and the repayment period?
Since you want the furniture now, this involves a PV
PMT
PV = $2250 Once you repay the loan, FV = 0 Payments are deferred for 11 months.
DEFERRAL
Finding Payment Size in a
Deferred Annuity
Finding Payment Size in a
Deferred Annuity
11-2611111111
McGraw-Hill Ryerson©
York Furniture has a promotion on a bedroom set selling for $2250. Buyers will pay “no money down and no payments for 12 months.” The first of 24 equal monthly payments is due 12 months from the purchase date.
What should the monthly payments be if York Furniture earns 10% compounded monthly on its account receivable during both
the deferral period and the repayment period?
York Furniture has a promotion on a bedroom set selling for $2250. Buyers will pay “no money down and no payments for 12 months.” The first of 24 equal monthly payments is due 12 months from the purchase date.
What should the monthly payments be if York Furniture earns 10% compounded monthly on its account receivable during both
the deferral period and the repayment period?
In effect, York furniture has
given a loan to a buyer of $2,250 on the day of the sale!
In effect, York furniture has
given a loan to a buyer of $2,250 on the day of the sale!
When the payments begin, the buyer owes $2,250
plus accrued interest!
When the payments begin, the buyer owes $2,250
plus accrued interest!
11-2711111111
McGraw-Hill Ryerson©
d = 11i = 0.10/12
n = 24
$2250 PMT PMT PMT Payments
$2250
PVAnnuity
FV
PV of the payments at the end of month 11
PV of the payments at the end of month 11
FV of the $2,250 loan at the end of month 11
FV of the $2,250 loan at the end of month 11
=
Months0 11 12 13 35 36
11-2811111111
McGraw-Hill Ryerson©
11
12
FV = 2,465.06
10 0
Find the amount owed after 11 months:
2250
$2,465.06 is the PV of the annuity$2,465.06 is the PV of the annuity
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period?
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period?
Finding Payment Size in a
Deferred Annuity
Finding Payment Size in a
Deferred Annuity
11-2911111111
McGraw-Hill Ryerson©
2465.0624
FV = 2,465.06
Now find the PMT of the annuity …
0
24 monthly payments of $113.75 will repay the loan.
24 monthly payments of $113.75 will repay the loan.
PV = - 2,465.06PMT = 113.75
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period?
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period? Formula solutionFormula solution
Finding Payment Size in a
Deferred Annuity
Finding Payment Size in a
Deferred Annuity
11-3011111111
McGraw-Hill Ryerson©
FV = PV(1 + i)nFormula Formula
FV = 2250(1 + 0.10/12)11
= $2,465.06
2465.06
i
-ni)PMTPV
(11[ ]= PMT [1-(1+.10/12)-24]
.10/12= $113.75PMT
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period?
York Furniture
has a promotion on a bedroom set selling
for $2250. Buyers will pay “no money down and no
payments for 12 months.” The first of 24
equal monthly payments is due 12 months from the
purchase date. What should the monthly payments be if York
Furniture earns 10% compounded monthly on
its account receivable during both the deferral
period and the repayment period?
24 monthly payments of $113.75 will repay the loan.
24 monthly payments of $113.75 will repay the loan.
Find the amount owed after 11 months:
Finding Payment Size in a
Deferred Annuity
Finding Payment Size in a
Deferred Annuity
11-3111111111
McGraw-Hill Ryerson©
i.e....Number Of Payments
11-3211111111
McGraw-Hill Ryerson©
$20,000 is invested in a fund earning 8% compounded quarterly. The first quarterly withdrawal of $1,000 will be taken from the fund five years from now. How many
withdrawals will it take to deplete the fund?
N
Payments are deferred for 19 quarters
DEFERRAL
Finding Number Of Payments in a
Deferred Annuity
Finding Number Of Payments in a
Deferred Annuity
The FV of $20,000 after the deferral, becomes the PV of the annuity ...
11-3311111111
McGraw-Hill Ryerson©
Years0 4.75 5 6 7 8
d = 19$20,000
PV1
n = ?
This FV1 then becomes the PV of the annuity of $1000/quarter
The $20000 earns
interest for 4 years 9 months
Payments of $1000/quarter
FV1
i = 0. 08/4 = .02PMT = $1000
11-3411111111
McGraw-Hill Ryerson©
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
19
48 0
Find the FV of $20,000 in 4.75 years
20000
$29,136.22 is the PV of the annuity$29,136.22 is the PV of the annuity
FV = 29,136.22
Finding Number Of Payments in a
Deferred Annuity
Finding Number Of Payments in a
Deferred Annuity
11-3511111111
McGraw-Hill Ryerson©
1000
Now find the PMT of the annuity …
0
44.1 quarterly payments will deplete the fund(44 full payments and 1 partial)
44.1 quarterly payments will deplete the fund(44 full payments and 1 partial)
29136.22
FV = 29,136.22PV = - 29136.22N = 44.1
Formula solutionFormula solution
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
Finding Number Of Payments in a
Deferred Annuity
Finding Number Of Payments in a
Deferred Annuity
11-3611111111
McGraw-Hill Ryerson©
FV = PV(1 + i)nFormula Formula
FV = 20000(1 + 0.08/4)19
= $29,136.22
Find the FV of $20,000 in 4.75 years
PMTPV *i
i1ln
1lnn
[ ]
ln(1.02)
= 44.1 payments or 11 years
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
$20,000 is invested in a fund earning 8% compounded
quarterly. The first
quarterly withdrawal
of $1000 will be taken from the fund five years
from now. How
many withdrawals will it
take to deplete the fund?
Finding Number Of Payments in a
Deferred Annuity
Finding Number Of Payments in a
Deferred Annuity
[ln 1 - ]29136.22 *.021000
11-3711111111
McGraw-Hill Ryerson©
When…number of compoundings per year
number of payments per year
11-3811111111
McGraw-Hill Ryerson©
Since you get paid every second Thursday you
decide to pay $350 every two weeks
to make your budgeting easier.
Find the new term of your mortgage if the interest charges
remain at 5% compounded
monthly.
12
26350
P/Y = 26
415 bi-weekly payments or 15 yrs 11.4 months
415 bi-weekly payments or 15 yrs 11.4 months
C/Y= 12PMT = -350N = 414.74
Formula solutionFormula solution
11-3911111111
McGraw-Hill Ryerson©
Since you get paid every second
Thursday you decide to pay $350
every two weeks to make your
budgeting easier. Find the new term of your mortgage
if the interest charges remain at 5% compounded
monthly.
Determine c Step 1Step 1
C= 12 / 26 = .4615
i2 = (1+i)c - 1
i2 = (1+ .05/12) .4615-1
i2 = 0.0019
Use c to determine i2 Step 2Step 2
C =number of compoundings per year
number of payments per year
Step 3Step 3
11-4011111111
McGraw-Hill Ryerson©
as the value for “i” in the appropriate annuity formula
Step 3Step 3 Use this rate i2 = 0.0019
FormulaFormula iPMT
PV i*
1ln
1ln[ ]n
1.0019 0.00190.5428-0.4571-0.7828
1
350100 000
1
0.0019-414.74
415 payments or 15 yrs 11.4 months415 payments or 15 yrs 11.4 months
11-4111111111
McGraw-Hill Ryerson©
# of Payments
# of Payments
PaymentAmountPaymentAmount Total CostTotal CostScenarioScenario
1.
2.
$100,000 Twenty-year Mortgage – Interest 5% per annum
$100,000 Twenty-year Mortgage – Interest 5% per annum
$659.96 $158,390.40
$152,264.00
$149,074.50
$700.00
3. $725.00
$145,250.004. $350.00
TermsTerms
Per month
Per month
Per month
Every two
weeks
240
218
206
415 $145,250.004. Every two
weeks415
Best Scenario
11-4211111111
McGraw-Hill Ryerson©
350
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If
you save $350 per pay, how long would it take to have an additional
$15000, if you can earn 8% compounded
monthly on your savings?
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If
you save $350 per pay, how long would it take to have an additional
$15000, if you can earn 8% compounded
monthly on your savings?
12
26
150000
N = 40.32
8
= FV = FV
New requiredNew requiredFormulaFormula
11-4311111111
McGraw-Hill Ryerson©
Determine c Step 1Step 1
C= 12 / 26 = .4615
i2 = (1+i)c - 1
i2 = (1+ .08/12) .4615-1
i2 = 0.0031
Use c to determine i2 Step 2Step 2
C =number of compoundings per year
number of payments per year
Step 3Step 3
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If you save $350 per
pay, how long would it take to have
an additional $15000, if you can earn 8%
compounded monthly on your
savings?
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If you save $350 per
pay, how long would it take to have
an additional $15000, if you can earn 8%
compounded monthly on your
savings?
11-4411111111
McGraw-Hill Ryerson©
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If you save $350 per
pay, how long would it take to have
an additional $15000, if you can earn 8%
compounded monthly on your
savings?
You are now considering delaying the purchase of your first house to
allow for a larger down payment. If you save $350 per
pay, how long would it take to have
an additional $15000, if you can earn 8%
compounded monthly on your
savings?
15000
1
1.00310.00310.13161.1316
FormulaFormula n iPMT
FV i*
1ln
1ln[ ]+
0.1237 0.003140.3
40.3 bi-weekly payments = approx 1yr 7months
40.3 bi-weekly payments = approx 1yr 7months
1
350
11-4511111111
McGraw-Hill Ryerson©
1. Base formula
iPMTFV
ni)(1 1[ ]2. To isolate n, divide both
sides by PMT PMTPMT
…continued……continued…
Developing the FormulaFormula
PMTFV
FormulaFormula iPMT
FV i*
1ln
1ln[ ]n
+
i
PMTFV ni)(1 1[ ]
i ni)(1 1[ ]
11-4611111111
McGraw-Hill Ryerson©
…from 2. PMTFV
i ni)(1 1[ ]
(a) Multiply both sides by i 3. Continue to isolate n …
PMTFV
i ni)(1 1[ ] *i *i
[ ]PMT FV
ni)(1 1 *i
(b) Reorganize equation PMT FV ni)(1 1 *i
(c) Now Take the natural logarithm (ln or lnx) of both sides
n ln(1+ i) ln[ ]PMT * iFV1 +
(d) Solving for n… divide both sides by
ln(1+i)ln(1+i) ln(1+i)
n ln(1+ i) ln[ ]PMT * iFV1 +
PMTFV * i
i1ln
1 +lnn
[ ]
11-4711111111
McGraw-Hill Ryerson©
You already have
$10000 saved for your down
payment. If you save $350 per pay,
how long would it take to have an additional $15000?
Assume you can earn 8%
compounded monthly on all of your savings.
You already have
$10000 saved for your down
payment. If you save $350 per pay,
how long would it take to have an additional $15000?
Assume you can earn 8%
compounded monthly on all of your savings.
12
26
Already enteredAlready entered
N = 37.25
350
10000
25000
8
37.5 bi-weekly payments = approx 1 yr 5months
37.5 bi-weekly payments = approx 1 yr 5months
11-4811111111
McGraw-Hill Ryerson©
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
Already enteredAlready entered
12
26
FV = 31430.12
10000
52
8
Formula solutionFormula solution
350
11-4911111111
McGraw-Hill Ryerson©
3 Steps
Formula SolutionFormula Solution
This is more complicated to solve when
using algebraic equations!
1.1.
2.2.
3.3.
Find the FV of the $10 000 in 2 years
Find the FV of the $350 per pay
Add totals together
The $10 000 continues to earn interest during the new savings period!
The $10 000 continues to earn interest during the new savings period!
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
11-5011111111
McGraw-Hill Ryerson©
Formula SolutionFormula Solution
FV = PV(1 + i)nFormula Formula
= 10000(1 + 0.08/12) 24
= $11,728.88
1.1.
2.2.
i2 = (1+i)c - 1= (1+ .08/12).4615-1
= 0.0031
3.3.
$11,728.88
= 350 [(1+.0031)52 –1].0031
= $19701.24 19,701.2431,430.12Total
PMTFV
i ni)(1 1[ ]
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
You already have
$10000 saved for your down
payment. If you save $350 per pay, for the next 2 years, find the size of your available down
payment. Assume you can earn 8%
compounded monthly on all of your savings.
11-5111111111
McGraw-Hill Ryerson©
11-5211111111
McGraw-Hill Ryerson©
A life insurance company advertises that $50,000 will purchase a 20-year annuity
paying $341.13 at the end of each month.
What nominal rate of return does the annuity investment earn?
A life insurance company advertises that $50,000 will purchase a 20-year annuity
paying $341.13 at the end of each month.
What nominal rate of return does the annuity investment earn?
1
12
341.13240
050000
C/Y = 1I/Y = 5.54
The annuity earns 5.54% paThe annuity earns 5.54% pa
11-5311111111
McGraw-Hill Ryerson©
…to solve for i without
a financial calculator
11-5411111111
McGraw-Hill Ryerson©
This completes Chapter 11This completes Chapter 11