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Unformatted text preview: What amount must firm repay after 4 years? 14 Compound Interest I Interest is not only earned on the amount initially invested but also on any accrued interest. – You earn interest on interest I With compound interest, money grows exponentially instead of linearly I Small differences in the rate of return can have large impact on profits over long periods of time 15 How Compound Interest Works I An Example: Assume you invest P = $100 at an annual rate of interest r = 5% for n = 4 years. You take no money out of your account before the end of year 5. – After 1 year, the future value of P, denoted by FV 1 is given by – From the end of year 1 to the end of year two, the $105 will grow at 5%, i.e. – After 3 years, you will have: – By repeated multiplication, you will find the value after 4 years to be: 16 General Compound Interest Formula I An investment of PV that is invested at a periodic rate of return of r grows to FV n after n periods, i.e. I Where: n = number of time periods for which interest is earned Note: n does not have to be ‘ years ’ r = effective periodic interest rate 17 Example I Suppose at age 20 you decide to save for your retirement. You plan to put $100 into an account paying 8% interest pear year for 45 years. – Assume you earn simple interest only. How much money will you have after 45 years? – Assume now that you earn compound interest. How much money will you have after 45 years?...
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 Winter '10
 E.Fowler
 Time Value Of Money, Interest

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