Chapter 8, Problem 62SGR

To determine

To find: The time required to make the money triple.

Answer to Problem 62SGR

It will take $17.1656$ months.

Explanation of Solution

Given:

The rate of interest is $6.4\%$ .

The deposit is $\$2000$ .

Calculation:

Substitute $\$6000$ for $A$ , $\$2000$ for $P$ and $0.064$ for $r$ in the formula $A=P{e}^{rt}$ to find the time.

  $\begin{array}{c}6000=2000e^{0.064t}\\ e^{0.064t}=\frac{6000}{2000}\\ e^{0.064t}=3\end{array}$

Take $\ln$ on both sides of the above equation.

  $\begin{array}{c}\ln e^{0.064t}=\ln 3\\ 0.064t=\ln 3\\ t=\frac{\ln 3}{0.064}\\ \approx 17.1656\end{array}$

Therefore, it will take $17.1656$ months.