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Unformatted text preview: 32 Compound Interest •you place $100 (your principal) in the bank.•it earns 10% per year compound interest. •what amountdo you have after 2 years?THECALCULATION:•at the end of one year you will have: 100 + 100(.10) = 100(1 + .10) = $110•at the end of two years you will have: 110 + 110(.10) =110(1 + .10) = 100(1 + .10)2= $121THEKEYELEMENT:•at the end of each year . . . •the interest is added to the principal•and you start earning interest on the interest!•this property is the defining feature of compound interest32p. 1Compound Interest as an Exponential FunctionGrowth multiplierof an account:•what you multiply the amount in the account •at the beginning of yearby •to get new amount at the end of a yearExample: at 10%, if we start with $100, we end with 100 + (.10)100 = 100(1 + .10) = $110 so the growth multiplier of a 10% account is (1 + .10). This same growth multiplier will be in effect throughout the lifetime of the account (as long as the rate remains 10%).(amount at beginningof year n) x (1 + .10)=(new amount at endof year n)32p. 2We can now apply the "growth multiplier" approach to compute what the value of our account at the end ofany year:At end of yearwe have(old amt) x (growth mult)which iswhich is1 100(1 + .10)100(1 + .10)1$110.002 100(1 + .10)(1 + .10)100(1 + .10)2$121.003100(1 + .10)2(1 + .10)100(1 + .10)3$133.10…20 Follow the pattern100(1 + .10)20$672.75$672....
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff

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