Chapter 12.4, Problem 16E

To determine

To find: The amount of monthly payment.

Answer to Problem 16E

The amount of monthly payment is $811.41.

Explanation of Solution

Given:

Mortgage Amount = $80,000

Interest Rate = 9% per year (or 0.75% monthly)

Number of Payments = 15 years (or 180 months)

Formula:

$R=\left[\frac{i{A}_p}{1-{\left(1+i\right)}^{-n}}\right]$

Here,

A_p = Present Value

R = Periodic Payment

i = Interest Rate

n = Number of Years/Payments

Mortgage: A mortgage is considered as a guarantee or a security for a loan on property or real estate. The mortgagor enters into an agreement with a mortgagee to receive loan amount initially and repay the loan during a specified time period and interest rate.

Calculation:

The amount of each payment is calculated by multiplying the present value with interest rate and the result is divided by 1 minus, 1 plus interest rate to the power minus number of years.

$\begin{array}{c}R=\left[\frac{i{A}_p}{1-{\left(1+i\right)}^{-n}}\right]\\ =\left[\frac{\left(\frac{9\%}{12}\right)\times \$80,000}{1-{\left(1+\left(\frac{9\%}{12}\right)\right)}^{-15\times 12}}\right]\\ =\left[\frac{0.75\%\times \$80,000}{1-{\left(1+0.75\%\right)}^{-180}}\right]\\ =\left[\frac{\$600}{1-0.2605}\right]\end{array}$

$\begin{array}{c}=\left[\frac{\$600}{0.7395}\right]\\ =\$811.4133or\$811.41\end{array}$

Therefore the Amount of monthly payment is $811.41.