Chapter 4.4, Problem 1MRPS

Solution

a.

How much interest does each account earn?

The solution is shown in the table..

Given information:

A three year CD that requires a minimum balance of $\$1500$ .The annual interest $2\%$

A five year CD that requires a minimum balance of $\$2000$ .The annual interest $3\%$

Concept Used:

Use the formula: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Where,

P= start amount

r= Rate

n= Times compounded per period of t

t=time

Calculation:

As per the given problem.

A three year CD that requires a minimum balance of $\$1500$ .The annual interest $2\%$

Use the formula, and substitute the values,

  $\begin{array}{l}A=1500{\left(1+\frac{0.02}{12}\right)}^{12\left(3\right)}\\ A=1500{\left(1+\frac{0.02}{12}\right)}^{36}\\ A=1592.68\end{array}$

Interest $=\$92.68$

A five year CD that requires a minimum balance of $\$2000$ .The annual interest $3\%$

  $\begin{array}{l}A=2000{\left(1+\frac{0.03}{12}\right)}^{12\left(5\right)}\\ A=2323.23\end{array}$

Interest $=\$323.23$

Conclusion:

Hence, for $2\%$, amount $=1592.68$ and interest $=\$92.68$

  $3\%$ , amount $=2323.23$ and interest $=\$323.23$

b.

What is the difference in the amount of interest..

  $=230.55$

Given information:

Note that from the part (a) interest $=\$92.68$ and interest $=\$323.23$

Concept Used:

Subtract the smaller interest from the larger interest amount.

Calculation:

As per the given problem

Now use the formula,

Subtract the smaller interest from the larger interest amount.

  $\begin{array}{l}=323.23-92.68\\ =230.55\end{array}$

Conclusion:

Therefore difference in the amount of interest is $230.55$.

c.

Describe the benefits and draw back of each account.

The benefits and drawback is in the explanation.

Given information:

A three year CD that requires a minimum balance of $\$1500$ .The annual interest $2\%$

A five year CD that requires a minimum balance of $\$2000$ .The annual interest $3\%$

Concept Used:

Use the formula: $A=P{\left(1+\frac{r}{n}\right)}^{nt}$

Where,

P= start amount

r= Rate

n= Times compounded per period of t

t=time

Explanation:

Note that the first CD requires a smaller deposit amount $1500$ and has a shorter period ( $3$ years) where the investor cannot access their money. The drawback of this, however, is that the investor makes less money ( $2\%$ interest rate).

The second CD requires a higher deposit $\left(2000\right)$ and a longer period ( $5$ years) where the investor cannot access their money.

However the account offers a higher $3\%$ interest rate.

Conclusion:

The benefits and drawback is above in the explanation.