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.
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
To estimate how much time it would take to double Joan's investment using the Rule of 72, you need to divide the number 72 by the interest rate. In this case, the interest rate for Bank A is 3.10%.
To apply the Rule of 72, divide 72 by 3.10%:
72 / 3.10 = 23.23
This means that it would take approximately 23.23 years for Joan's investment to double at Bank A's interest rate.