Chapter 4.5, Problem 5E

Reminder Round all answers to two decimal places unless otherwise indicated.

Doubling Time If an investment earns an APR of $r$, as a decimal, compounded annually, then the time $D$, in years, required for the investment to double in value is given by

$D=\frac{\log 2}{\log \left(1+r\right)}$.

a. Find the doubling time for an investment subject to an APR of $5\%$ if interest is compounded annually.

b. Plot the graph of the doubling time $D$ versus the interest rate $r$, as a decimal. Use a horizontal span of $0$ to $0.1$.

c. Does a small change in the interest rate have a greater effect on the doubling time if interest rates are low or if they are high?