Question

Suppose that ​$150,000.00 is owed on a house. The monthly payment for principal and interest at 10.0​% for 30 years is 150•$8.77572 = $1316.36.

The total interest charged is the total amount paid minus the amount financed. What is the total interest that will be​ paid?

Answer 1

In this case,

P = $150000

r = 10% = 0.10

t = 30 years

n = 12 [Compounded monthly]

Therefore,

Monthly payment

= rP/ n[1 - (1 + (r/n))^-nt]

= (0.10 * 150000) / 12[1 - (1 + (0.10/12))^{-12 * 30}]

= (0.10 * 150000) / 12[1 - (1 + (0.10/12))^-360]

= $1316.36

Total amount paid

= Monthly payment * n * t

= $1316.36 * 12 * 30

= $473889.60

Total interest that will be paid

= $473889.60 - $150000

= $323889.60