Chapter 6.4, Problem 25Q

(a)

To determine

To find the money in each account and the interest that each account earn.

Explanation of Solution

Given:

A local bank advertises two certificate of deposit (CD) accounts that you can use to save money and earn interest. The interest is compounded monthly for both accounts.

Calculation:

The amount of money in the first account at the end of the month-

  $\begin{array}{l}{\mathrm{A}}_1={\mathrm{P}}_1{\left(1+\frac{{\mathrm{r}}_1}{12}\right)}^{12{\mathrm{t}}_1}\\ {\mathrm{A}}_1=1500{\left(1+\frac{0.02}{12}\right)}^{3\cdot 12}\\ {\mathrm{A}}_1=1500{\left(1.0017\right)}^{36}\\ \approx 1592.68\end{array}$

The interest in the first account at the end of its term:

  $1592.68-1500=92.68$

The amount of money in the second account at the end of the month-

  $\begin{array}{l}{\mathrm{A}}_2={\mathrm{P}}_2{\left(1+\frac{{\mathrm{r}}_2}{12}\right)}^{12{\mathrm{t}}_2}\\ {\mathrm{A}}_2=2000{\left(1+\frac{0.02}{12}\right)}^{5\cdot 12}\\ {\mathrm{A}}_2=2000{\left(1.0025\right)}^{60}\\ \approx 2323.23\end{array}$

The interest in the second account at the end of its term:

  $2323.23-2000=323.23$

(b)

To determine

To describe the benefits and drawbacks of each account.

Explanation of Solution

The first account has the advantages of a smaller segment of time and a smaller deposit and the disadvantage of a smaller interest.

The second account has the advantage of paying a better interest, but the deposit is greater than the segment of time longer.