Chapter SH, Problem 7.25EP

a.

To determine

To find the time taken by Stefanie to have a balance of $\$2400$ .

Answer to Problem 7.25EP

  $0.61$ years.

Explanation of Solution

Given:

Stefanie deposited $\$25000$ at the interest rate of $2.5\%$ .

Calculation:

Using the formula of compound interest to find out the time as follows-

  $\begin{array}{l}2400=2000e^{\frac{2.5}{100}t}\\ 1.2=e^{0.025t}\\ \ln 1.2=0.025t\\ t=\frac{\ln 1.2}{0.025}\end{array}$

Solve further:

  $\begin{array}{l}t=7.29\text{ months}\\ t\approx \text{0}\text{.61 years}\end{array}$

Hence, it will take $0.61$ year to have a balance of $\$2400$ .

b.

To determine

To find how much time Stefanie will take to double her investment.

Answer to Problem 7.25EP

  $2.31\text{ years}$ .

Explanation of Solution

Given:

Stefanie deposited $\$25000$ at the interest rate of $2.5\%$ .

Calculation:

  $\begin{array}{l}4000=2000e^{\frac{2.5}{100}t}\\ 2=e^{0.025t}\\ \ln 2=0.025t\\ t=\frac{\ln 2}{0.025}\\ t=2.31\text{ years}\end{array}$

Hence, it will take $2.31\text{ years}$ to double the investment.

c.

To determine

To find the investment amount if Stefanie wants to have $\$5000$ after $10$ years.

Answer to Problem 7.25EP

  $\$3894$ .

Explanation of Solution

Given:

Stefanie deposited $\$25000$ at the interest rate of $2.5\%$ .

Calculation:

The amount to have $\$5000$ after $10$ years as follows-

  $\begin{array}{l}5000=P{e}^{\frac{2.5}{100}\times 10}\\ 5000=P{e}^{0.25}\\ P=\frac{5000}{e^{0.25}}\\ P=\$3894\end{array}$

Hence, the amount to have $\$5000$ after $10$ years is $\$3894$