3-2 - 3-2 Compound Interest •you place $100(your...

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Unformatted text preview: 3-2 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 interest3-2p. 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)3-2p. 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.

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3-2 - 3-2 Compound Interest •you place $100(your...

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