COMM
Class 6 and 7 Before

# O so to wrap it up and that s the only thing you

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O So to wrap it up – and that s the only thing you really need to know: <DRUMROLLS> O For an interest rate ‘r’, the present value of an annuity with n level cash flows ‘A’ that start at the end of the first period is equal to:

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24 Old Example: Present Value of an Annuity O Recall the example from before: Four cash flows of \$1,000 Interest rate is 10% per year. O Timeline: 0 1 2 3 4 Periods -----|----------|----------|----------|----------|--------------- PV = ? 1,000 1,000 1,000 1,000 Cash Flows
25 Car Buying Example O You start a new job and think you have enough money to pay \$500 per month for a new car. Suppose the car dealerships right now offer to lend money at 12% per year compounded monthly for 48 months with a zero downpayment. How much can you spend on a car today? Assume the first payment is due exactly one month after you buy the car. Timeline:

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26 Example: Future Value of an Annuity O How much money would your sister have four years from now if she saved the money she got from your grandparents? O Timeline: 0 1 2 3 4 Periods -----|----------|----------|----------|----------|--------------- 1,000 1,000 1,000 1,000 Cash Flows
27 In General: Future Value of an Annuity O Consider an n-period annuity, where payments of A are made at the end of each period. The periodic effective interest rate is r. Then the future value of the annuity is given by:

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28 Car Buying Example Cont d
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• Spring '10
• E.Fowler

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