Chapter 12.7, Problem 12CFU

a.

To determine

Find the return on investment after $5Years$ .

Answer to Problem 12CFU

  $1.345P$

Explanation of Solution

Given information:

A saving account with a $6\%$ interest rate compounded continuously. Morgan needs to double the amount she will deposit over $5Years$ .If she deposits $Pdollars$ .

Calculation:

Consider the formula for continuous compounding interest,

  $\begin{array}{l}A=P{e}^{rt}\\ A=P{e}^{0.06\times 5}\\ A=P{e}^{0.3}\\ u\sin gthreetermsof\exp onentailseries,\\ A=P\left(1+0.3+\frac{{0.3}^2}{2}\right)\\ A\approx 1.345P\end{array}$

Hence, the return on investment after $5Years$ will be $1.345P$ .

b.

To determine

Explain that she double her money in desired amount of time.

Answer to Problem 12CFU

No.

Explanation of Solution

Given information:

A saving account with a $6\%$ interest rate compounded continuously. Morgan needs to double the amount she will deposit over $5Years$ .If she deposits $Pdollars$ .

Calculation:

The return on investment after $5Years$ is $1.345P$ it should be $2P$ after $5Years$ .

Hence, she cannot double the amount in desired time.

c.

To determine

Check the approximate amount with calculator and compare with approximate value.

Answer to Problem 12CFU

The approximation is accurate up to two decimal places.

Explanation of Solution

Given information:

A saving account with a $6\%$ interest rate compounded continuously. Morgan needs to double the amount she will deposit over $5Years$ .If she deposits $Pdollars$ .

Calculation:

By using a calculator we have,

  $e^{0.3}\approx 1.349$

And approximate value that we found in part $\left(a\right)$ was $e^{0.3}\approx 1.345$ .

Hence, the approximation is accurate up to two decimal places.