Suppose Joan has $5,000 to invest. The banks are offering 3.10% interest. Bank A compounds interest continuously, while Bank B compounds interest semiannually.

Use the Rule of 72 to estimate how much time it would take to double Joan's investment in Bank A.

1 answer

The rule of 72 is not exact, but does provide a good estimate for both banks A and B.

According to the rule of 72, the number of years needed to double, Y, is given by 3.1 * Y = 72

Y = 23.2 years.

The exact answers are:
Bank B: (1.0155)^(2Y) = 2
Y = 22.53 years -> 23 years
(The principle won't quite double in 22.5 years, so you will have to wait anther 6 months for the next interest payment)

Less time will be required with continuous compounding.

Bank A: See
http://www.moneychimp.com/articles/finworks/continuous_compounding.htm

e^(Y*.031) = 2
Y = 22.36 years