Chapter 8.5, Problem 58E

a.

To determine

To find: the balance after the fourth payment.

Answer to Problem 58E

  $a_4=\$9684.05$ .

Explanation of Solution

Given:

The borrow amount of $\$10,000$ at $11.5\%$ annual interest compounded monthly for 7 years.

Calculation:

As the borrow amount of $\$10,000$ at $11.5\%$ annual interest compounded monthly for 7 years. Then

  $\begin{array}{l}\text{priciple}=\$10,000\\ \text{Rate of interest}=\frac{11.5}{12}\%=0.0096\end{array}$

Therefore, $a_n=1.0096a_{n-1}-173.86$

Now, to find the balance after the fourth payment, therefore,

  $a_4=1.0096a_3-173.86=9684.05$

Hence, the amount after the fourth payment is $a_4=\$9684.05$ .

b.

To determine

To find: the balance of the last payment.

Answer to Problem 58E

  $a_{84}=\$14.37$ .

Explanation of Solution

Given:

The borrow amount of $\$10,000$ at $11.5\%$ annual interest compounded monthly for 7 years.

Calculation:

From part (a) $a_n=1.0096a_{n-1}-173.86$

Now, to find balance of the last payment,

As the total time is 7 years or 84 months, then

  $a_{84}=1.0096a_{83}-173.86=\$14.37$

Hence, the amount of the last payment is $a_{84}=\$14.37$ .