Chapter 12.4, Problem 17E

To determine

The monthly payment and total payment on 30 years mortgage.

Answer to Problem 17E

The monthly payment is $733.76 and the total amount paid is $264,155.25.

Explanation of Solution

Monthly payment is the amount a borrower needs to pay every month until a debt is paid off. Usually monthly payments are specified in the loan document regarding how they are calculated, their due date and what happens if the situation is made as pre-agreed.

Formula of monthly payment:

$\text{Monthly}\text{payment}\text{=}\frac{i\times \left(A_p\right)}{1-{\left(1+i\right)}^{-n}}$

Where,

i= interest amount

$A_p$ = borrowing amount

$n$= period

Calculation:

Calculate the monthly payment amount:

$\begin{array}{c}\text{Monthly}\text{payment}\text{=}\frac{i\times \left(A_p\right)}{1-{\left(1+i\right)}^{-n}}\\ =\frac{\frac{8\%}{12}\times \left(\$100,000\right)}{1-{\left(1+\frac{8\%}{12}\right)}^{-30\times 12}}\\ =\frac{0.006667\times \left(\$100,000\right)}{1-{\left(1+0.006667\right)}^{-360}}\\ =\frac{666.6667}{0.908557}\end{array}$

                                    $=\$733.76$

Therefore, the monthly payment is $733.76.

Calculate the total amount to be paid.

$\begin{array}{c}\text{Total}\text{amount}\text{paid}\text{=}\text{Monthy}\text{payment×}\text{Period}\\ =\$733\times \left(30\times 12\right)\\ =\$264,155.25\end{array}$

Therefore, total amount paid is $264,155.25.