Comparing Compound Interest.
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The Problem |
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Suppose $1000 is deposited by a 20-year-old worker in an Individual
Retirement Account (IRA) that pays an annual interest rate of 12%. Describe
the effect on the balance at age 65, if the interest were compounded |
Recall the formula for compound interest is 
where,
| P = initial deposit t = time in years r = rate of interest as a decimal n = number of compounding periods in one year A = the amount in the account after t years |
From the given information, P = 1000, t = 65 - 20 = 45, and r = .12.
a). Compounded annually means n = 1 (one compounding period in one year).
So 
= $163,987.60.
b). Compounded quarterly means that n = 4 (4 compounding periods
in one year). So 
= $204,503.36.
Obviously, the quarterly compounding will yield a significantly greater amount of money.
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