Question

Andrew is financing a condominium for $543,000. He gets a 30-year, fixed rate mortgage with a rate of 5.475%. How much interest will he pay over the life of his loan? Round to the nearest dollar

Answer 1

$563 850

Explanation:

A. Monthly payment

The formula for the monthly payment (P) on a loan of A dollars that is paid back in equal monthly payments over n months, at an annual interest rate of i % is

`P = A((i)/(1-(1+i)^(-n)))`

Data:

We must express the interest rate on a monthly basis.

i = 5.475 %/yr = 0.456 25 %/mo = 0.004 5625

A = $543 000

n = 360 mo

Calculation:

`P = 543 000((0.004 5625)/(1-(1+0.004 5625)^(-360)))`

`P = \frac{2477.34}{{1- {1.004 5625}}^(-360)}`

`P = (2477.34)/(1 - 0.194 220)`

`P = (2477.34)/(0.805 780)`

P = $3074.583

B. Total Payment (T)

T = nP

T = 360 × 3074.583

T = $1 106 850

C. Total Interest (I)

I = T – A

I = 1 106 850 – 543 000

I = $563 850

Andrew's total interest is $563 850.