Asked by Anonymous
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.
Use the Rule of 72 to estimate how much time it would take to double Joan's investment in Bank A.
Answers
Answered by
drwls
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
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
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