Question

Abbey purchased a house using a fixed rate mortgage. The annual interest rate is 4.2% compounded monthly for 20 years. The mortgage amount is $235,000. What is the monthly payment on the mortgage? This isn't a multiple choice question sadly...I have to show my work

Answer 1

Answer:

Monthly payment is $1448.82

Step-by-step explanation:

Given : Abbey purchased a house using a fixed rate mortgage. The annual interest rate is 4.2% compounded monthly for 20 years. The mortgage amount is $235,000.

To find : What is the monthly payment on the mortgage?

Solution : First we find the monthly payment

Formula of monthly payment  

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$  

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$  

Where, Amount = $235,000

Rate r= 4.2%=0.042  

$i=\frac{0.042}{12}=0.0035$  

Time = 20 years  

$n=20\times12=240$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.0035)^{-240}}{0.0035}$  

$D=\frac{1-(1.0035)^{-240}}{0.0035}$  

$D=\frac{1-0.4323}{0.0035}$  

$D=\frac{0.5677}{0.0035}$  

$D=162.2$  

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$  

$M=\frac{235000}{162.2}$  

$M=1448.82$  

Approximately,monthly payment is $1448.82