Chapter 11.6, Problem 58E

a.

To determine

Find the time to double the money in the account.

Answer to Problem 58E

  $11years$ .

Explanation of Solution

Given information:

Jenny deposited money in an account for interest rate $6.3\%$ compounded continuously.

Calculation:

Consider the formula for continues compounding,

  $\begin{array}{l}A=P_o{e}^{rt}\\ A=2P_o\\ 2P_o=P_o{e}^{0.063t}\\ 2=e^{0.063t}\\ taking\log bothsides,\\ \ln 2=\ln e^{0.063t}\\ \ln 2=\ln e^{0.063t}0.063t\\ t=\frac{\ln 2}{0.063}=11.0023years\end{array}$

Hence, the time to double the money in the account is $11years$ .

b.

To determine

Approximate number of years to double the money.

Answer to Problem 58E

  $11.4years$ .

Explanation of Solution

Given information:

Jenny deposited money in an account for interest rate $6.3\%$ compounded continuously.

The rule of $72$ states that if you divide $72$ by the interest rate,

Calculation:

The rule of $72$ states that if you divide $72$ by the interest rate,

  $\frac{72}{6.3}=11.4years$

Hence, Approximate number of years to double the money is $11.4years$ .