A house sells for $282,500 and a 35% down payment is made. A 15-year mortgage at 7.5% was
Obtained. Find the monthly payment and the total interest paid.
A)Monthly payment = $1,704.04; total interest paid = $123,102.20
B)Monthly payment = $1,695.89; total interest paid = $121,635.20
C)Monthly payment = $1,713.15; total interest paid = $124,742.00
D)Monthly payment = $1,804.03; total interest paid = $141,100.40

Question

A house sells for $282,500 and a 35% down payment is made. A 15-year mortgage at 7.5% was
Obtained. Find the monthly payment and the total interest paid. 
A)Monthly payment = $1,704.04; total interest paid = $123,102.20 
B)Monthly payment = $1,695.89; total interest paid = $121,635.20 
C)Monthly payment = $1,713.15; total interest paid = $124,742.00 
D)Monthly payment = $1,804.03; total interest paid = $141,100.40

Quizplus · Accepted Answer

The amount of the down payment is:

282,500 x 0.35 = 98,875

So the amount of the mortgage is:

282,500 - 98,875 = 183,625

To find the monthly payment for a 15-year mortgage at 7.5%, we use the formula:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where:

M = monthly payment
P = principal (amount of the mortgage)
i = monthly interest rate (annual rate divided by 12)
n = number of payments

First, we find the monthly interest rate:

7.5 / 12 = 0.625%

Next, we find the total number of payments:

15 x 12 = 180

Now we can plug these values into the formula and solve for M:

M = 183,625 [ 0.00625(1 + 0.00625)^180 ] / [ (1 + 0.00625)^180 - 1]
M = $1,704.04

To find the total interest paid, we multiply the monthly payment by the number of payments and subtract the principal:

Total interest = (1,704.04 x 180) - 183,625
Total interest = $123,102.20

Therefore, the best choice is A.

A House Sells for $282,500 and a 35% Down Payment