Comparing Compound Interest.

The Problem

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
a) annually and
b)quarterly.

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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