COMM
Class 2 Jan 9th Before

# I interest payments are given by i rp each period

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I Interest payments are given by I =r*P each period, where r is the simple rate of interest I Over n periods, the original amount invested grows to I Example: Firm borrows \$100 at 5% simple interest due at the end of 4 years. What amount must firm repay after 4 years? 14

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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

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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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• Spring '10
• E.Fowler

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