Agenda 11/28

Review Quiz 4Discuss interest and the time value of moneyExplore the Excel time value of money

functionsExamine the accounting measures of

profitabilityCourse Evaluations

Introduction to Interest Calculations

When you borrow money you pay interestWhen you loan money, you receive interestWhen you make a payment

part of the payment is applied to interest Part of the payment is applied to principal

Understanding time value of money

Money will increase value over time if the money is invested and can make more money.

If you have $1,000 today, it will be worth more tomorrow if you invest that $1,000 and it earns additional money (interest or some other return on that investment).

If you have $1,000 today, it will NOT be worth more tomorrow if you put it in an envelope and hide it in a drawer. Then the time value of money does not apply. Of course, you won’t lose the $1,000 either…

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Types of Interest

Simple interest Interest is paid only on the principal Many certificates of deposit work this way

Compound interest Interest is added to the principal each period Interest is calculated on the principal plus any accrued

interest Compounding can occur on different periods

Annually, quarterly, monthly, daily

Difference between simple and compound interest

Assume that you have $1,000 to invest. $1,000 is the present value (PV) of your money.

You can invest it and receive “simple” interest or you can earn “compound” interest.

The money that you have at the end of the time you have invested it is called the “future value” (FV) of your money.

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Future value of money

Simple interest is always calculated on the initial $1,000. 5% interest on $1,000 is $50. Always $50.

When interest is paid on not only the principal amount invested, but also on any previous interest earned, this is called compound interest.

FV = Principal + (Principal x Interest) = 1000 + (1000 x .05) = 1000 (1 + i) = PV (1 + i)

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Simple vs. compound interest comparison

Year Simple Interest Compound Interest0 $1,000 $1,0001 $1,050 $1,0502 $1,100 $1,102.503 $1,150 $1,157.624 $1,200 $1,215.615 $1,250 $1,276.2810 $1,500 $1,628.8920 $2,000 $2,653.3030 $2,500 $4,321.94

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$1,000 Invested at 5% return

What about if you borrow money?

If you borrow money, the lender wants to earn “compound” money on its investment.

If you borrow $1000 at 10%, then you won’t pay back just $1,100 (unless you pay it back at once during the initial time period).

You will pay it back “compounded”. Interest will be calculated each period on your remaining balance.

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Amortization table $1,000 loan, pay $200 year, 10% year interest

Year Amount Owed Amount Plus Interest

Payment

1 $1,000.00 $1,100.00 $200.00

2 $900.00 $990.00 $200.00

3 $790.00 $869.00 $200.00

4 $669.00 $735.90 $200.00

5 $535.90 $589.49 $200.00

6 $389.49 $428.44 $200.00

7 $228.44 $251.28 $200.00

8 $51.28 $56.41 $56.41

Total Paid $1,456.41

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Types of financial questions usually asked

How much will it cost each month to pay off a loan if I want to borrow $150,000 at 6% interest each year for 30 years?

Assume that you need to have exactly $40,000 saved 10 years from now. How much must you deposit today in an account that pays 6% interest, compounded annually, so that you reach your goal of $40,000?

If you invest $2,000 today and have accumulated $2,676.45 after exactly five years, what rate of annual compound interest was earned?

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Some Excel financial functions

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Function DescriptionCUMIPMT Cumulative Interest PaymentsCUMPRINC

Cumulative Principal Payments

FV Future ValueIPMT Interest PaymentIRR Internal Rate of ReturnNPER Number of periodsNPV Net Present ValuePMT PaymentPPMT Principal PaymentPV Present ValueRATE Interest RateSLN Straight Line Depreciation

The PMT Function (Introduction)

PMT is used to calculate the periodic payment on a loan

The interest rate must be fixedThere may be a residual value on the note at

the end of the periods This is often referred to as a balloon payment An auto lease, for example, would have a residual note

value

The PMT Function (Arguments 1)

Rate: The first argument contains the interest rate per compounding period

Nper: The second argument contains the number of periods

PV: The third argument contains the present loan value FV: The fourth argument contains the future value

If the loan is paid off at the end of the periods, the value is 0 Type: The final argument indicates when payments are

made 0 (the default) indicates the end of the period 1 indicates the beginning of the period

The PMT Function (Arguments 2)

The PMT Function (Example)

Other Time Value of Money Functions

Here we are just solving the same equation for a different variable RATE determines the interest rate NPER determines the number of periods PMT determines the payment PV determines the present value of a transaction FV determines the future value of a transaction

The RATE Function (Introduction)

Determines the interest rate per period based on The number of periods The payment The present value The future value The type

The RATE Function (Arguments)

The RATE Function (Example)

The NPER Function (Introduction)

Determines the number of periods based on The interest rate The payment The present value The future value The type

The NPER Function (Arguments)

The NPER Function (Example)

The FV Function (Introduction)

Determines the future value of a lump sum It’s possible for FV to account for regular cash flows

(periodic payments) per period

The FV Function (Arguments)

The FV Function (Example)

The PV Function (Introduction)

Determines the present value of a cash flowLike FV, regular inflows or outflows are

supported

THE PV Function (Arguments)

The PV Function (Example)

The IPMT Function (Introduction)

Use IPMT to calculate the interest applicable to a particular period Use the initial balance for the present value no matter

the periodUse PPMT to calculate the principal applicable

to a particular periodThe arguments to both functions are the

same

The IPMT Function (Arguments)

The CUMIPMT Function (Introduction)

CUMIPMT calculates the cumulative interest between two periods

CUMPRINC calculates the cumulative principal between two periods

The arguments to both functions are the same

Functions require the analysis tool pack add-in

The CUMIPMT Function (Arguments)