TIME VALUE OF MONEY: Compound Interest.

With simple interest, the amount earned (for investedmoney) or due (for borrowedmoney in one period does not affect the principal for interest calculationsin laterperiods.However this is not how interest is normally calculated. In practice, interest is computed using the compound interest method. For a loan, any interest owed but not paid at the end of the year is added to the balance due. Thus, the next year's interest is calculated based on the unpaid balance due, which includes the unpaid interest fromthe preceding period. In this way, compound interest can be thought of as interest on top of interest.This distinguishe compound interest from simple interest. In this section, the remainder of the book, and in practice you should assume that the rate is a compound interest rate. The few exception will clearly state use "simple interest."


EXAMPLE  3-4 

To highlight the difference between simple and compoundinterest, reworkExample 3-3 using an interest rate of 8%per year compound interest.Howwill this change affect the amount that your friend pays you at the end of 5 years?

SOLUTION
Original loan amount (originalprincipal) = $5000
Loan term = 5 years
IntErest rate charged 8%per year cOlnpound interest

In the following table we calculate on a year-to-yearbasis the total dollar amount due at the end of each year. Notice that this amount becomes the principal upon which interest is calculated in the next year (this is the compounding effect).


The total amount due at the end of the fifth year, $7347, is the amount that your friend will give you to repay the original loan. Notice that this amount is $347more than the amount you received for loaning the same amount, for the same period, at simple interest. This, of course, is because of the effect of interest being earned (by you) on top of interest.


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