Chapter 8.2, Problem 45HP

To determine

To find what would be more beneficial from the two given cases.

Answer to Problem 45HP

The lower interest rate gives better deal than lower term of years.

Explanation of Solution

Given:

A $5$ year loan at $8\%$ interest compounded monthly.

The first case:If the term is reduced to $4$ years.

The second case: If the interest-rate is reduced to $6.5\%,$

Calculation:

Consider the case of a $5$ year loan at $8\%$ interest compounded monthly.

Let an amount of $\$100$ is invested.

The amount obtained after $5$ years is:

  $\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =100{\left(1+\frac{0.08}{12}\right)}^{12\times 5}\\ =148.98\end{array}$

If the term is reduced to $4$ years, the amount obtained is:

  $\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =100{\left(1+\frac{0.08}{12}\right)}^{12\times 4}\\ =137.56\end{array}$

If the interest-rate is reduced to $6.5\%,$ the amount obtained is:

  $\begin{array}{l}A=P{\left(1+\frac{r}{n}\right)}^{nt}\\ =100{\left(1+\frac{0.065}{12}\right)}^{12\times 5}\\ =138.28\end{array}$

Hence lower interest rate gives better deal than lower term of years.