Chapter 12.4, Problem 18E

To determine

To find: The amount of monthly payment and the total amount paid on loan.

Answer to Problem 18E

The amount of monthly payment is $1,687.71 and the monthly payment amount is $303,788.46.

Explanation of Solution

Given:

Mortgage Amount = $200,000

Interest Rate = 6% per year (or 0.50% 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

$\text{Total}\text{amount}\text{paid}=\left[\text{R}\times \text{n}\right]$

Here,

R = Periodic Payment

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.

$\begin{array}{c}R=\left[\frac{i{A}_p}{1-{\left(1+i\right)}^{-n}}\right]\\ =\left[\frac{\left(\frac{6\%}{12}\right)\times \$200,000}{1-{\left(1+\left(\frac{6\%}{12}\right)\right)}^{-15\times 12}}\right]\\ =\left[\frac{0.50\%\times \$200,000}{1-{\left(1+0.50\%\right)}^{-180}}\right]\\ =\left[\frac{\$1,000}{1-0.4075}\right]\end{array}$

$\begin{array}{c}=\left[\frac{\$1,000}{0.5925}\right]\\ =\$1,687.7137or\$1,687.71\end{array}$

Therefore, the amount of monthly payment is $1,687.71.

The total amount paid on loan is calculated by multiplying the monthly payments with the number of payments.

$\begin{array}{c}\text{Total}\text{amount}\text{paid}=\left[R\times n\right]\\ =\left[\$1,687.7137\times \left(15\times 12\right)\right]\\ =\left[\$1,687.7137\times 180\right]\\ =\$303,788.4581or\$303,788.46\end{array}$

Therefore, the amount of monthly payment is $303,788.46.