Class 2 Jan 9th Before

# I in the compound interest case how much interest do

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I In the compound interest case, how much interest do you earn on interest earned previously (interest on interest)? 18

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General Present Value Formula I In Finance, we often have to find today s value of (more or less certain) future cash flows. Said differently, we have to look for a present value. I From I We can easily get: n n r PV FV ) 1 ( * + = 19
Money Can Travel Through Time! I The Three Rules of Time Travel: 1. You can move (the value of) a cash flow forward in time by compounding it. 2. You can move a cash flow backward in time by discounting it. 3. To combine or compare values of cash flows that occur at different points in time, you have to bring them to the same point in time by compounding or discounting them. Where: PV 0 = present value (sometimes denoted by P for “Principal”) FV n = future value n periods from now n = the number of time periods over which interest accrues r = the effective periodic interest rate I = total amount of interest 20 FV n = PV 0 *(1 + r ) n PV 0 = FV n (1 + r ) n = FV n *(1 + r ) ! n

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Example: Discounting I You think you will need a new computer in three years. I You expect the computer to cost \$1,000 in three years. I If the annual interest rate you earn on your savings is 4%, how much money do you have to set aside today to be able to buy the computer in three year? 21
Example: The Third Rule of Time Travel (1) I Suppose we plan to save \$1,000 today, and \$1,000 at the end of each of the next two years. If we can earn a fixed 10% interest rate on our savings, how much will we have three years from today? 22

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Example: The Third Rule of Time Travel (2) I The time line would look like this: 23
Example: The Third Rule of Time Travel (3) 24
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• Spring '10
• E.Fowler

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