Chapter 12.4, Problem 31E

a.

To determine

To find how much J and M still owe on their mortgage.

Answer to Problem 31E

  $\$\text{80487}\text{.84}$

Explanation of Solution

Given:

$90000 mortgage at 9% interest, repayable over 30 years. They have made 120 payments.

Calculation:

There are 240 payments remaining. So, the present value of the money can be calculated as shown below.

  $\begin{array}{c}{A}_p=R\frac{1-{\left(1+i\right)}^{-n}}{i}\\ =724.17\frac{1-{\left(1+\frac{0.09}{12}\right)}^{-240}}{\left(\frac{0.09}{12}\right)}\\ =\$\text{80487}\text{.84}\end{array}$

b.

To determine

To calculate how much their next payment is interest and how much goes toward principal.

Answer to Problem 31E

Interest payment: $\$\text{603}\text{.66}$ .

Principal payment: $\$\text{120}\text{.51}$ .

Explanation of Solution

Given:

$90000 mortgage at 9% interest, repayable over 30 years. They have made 120 payments.

Calculation:

The remaining principal after 120 payment is $\$\text{80487}\text{.84}$ .

Since

  $\frac{9\%}{12}=0.75\%$ .

  $0.75\%$ of the principal will go toward interest each month.

So,

  $\begin{array}{c}\text{Interest payment = }0.75\%\text{ of}\$\text{80487}\text{.84}\\ \text{=}0.0075\times \$\text{80487}\text{.84}\\ =\$\text{603}\text{.6588}\\ \approx \$\text{603}\text{.66}\end{array}$

And, the principal payment will be $\text{\$}724.17-\$\text{603}\text{.66}=\$\text{120}\text{.51}$ .