Question

Don is buying a home for $190,300. He is making a 30% down payment and financing the rest with a 15-year loan at 5.75% interest. What will his monthly mortgage payment be?
a. $1106.18
b. $1124.16
c. $1304.28
d. $1580.25

Answer 1

The answer would be A. $1106.18

Answer 2

Answer:

Option A- $1106.18.

Step-by-step explanation:

Given : Don is buying a home for $190,300. He is making a 30% down payment and financing the rest with a 15-year loan at 5.75% interest.

To find : What will his monthly mortgage payment be?

Solution :

There is a 30% down payment

So, Amount financing $=190300-190300\times 30\%$

                                    $= 190300-190300\times0.3$

                                     $= 190300-57090=133210$

Formula of monthly payment  :

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

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

Where, Amount = $133210

Rate r= 5.75%=0.0575

$i=\frac{0.0575}{12}=0.00479$  

Time = 15 years  

$n=15\times12=180$  

Now, put all the values we get,  

$D=\frac{1-(1+i)^{-n}}{i}$  

$D=\frac{1-(1+0.00479)^{-180}}{0.00479}$  

$D=\frac{1-(1.00479)^{-180}}{0.00479}$  

$D=\frac{1-0.423}{0.00479}$  

$D=\frac{0.577}{0.00479}$  

$D=120.459$  

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

$M=\frac{133210}{120.459}$  

$M=1106.18$  

Therefore, Option A is correct.

The Monthly payment is $1106.18.