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

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3-2 Compound Interest you place \$100 (your principal ) in the bank. it earns 10% per year compound interest . what amount do you have after 2 years? T HE CALCULATION : 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 = \$121 THE KEY ELEMENT : 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 interest 3-2 p. 1

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Compound Interest as an Exponential Function Growth multiplier of an account: what you multiply the amount in the account at the beginning of year by to get new amount at the end of a year Example: 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 beginning of year n) x (1 + .10) = (new amount at end of year n) 3-2 p. 2
We can now apply the "growth multiplier" approach to compute what the value of our account at the end of any year: At end of year we have (old amt) x (growth mult) which is which is 1 100(1 + .10) 100(1 + .10) 1 \$110.00 2 100(1 + .10)(1 + .10) 100(1 + .10) 2 \$121.00 3 100(1 + .10) 2 (1 + .10) 100(1 + .10) 3 \$133.10 20 Follow the pattern 100(1 + .10) 20 \$672.75 n 100(1 + .10)

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

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