Comparing Compound Interest.
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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