Question

2. 2 years ago we purchased a house with a 30 year $525,000 mortgage at 9% A. What is the monthly payment? B. How much is owed after 2 years? C. How much interest did we pay over a 2 yr period? D. If we are looking to refinance and the current rate is 6.75% what would be the monthly payment on a 20yr and 15 yr mortgage.

Answer 1

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

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

a.

Loan = 525000

i = 9% = 9% / 12 = 0.75% per month

t = 30 * 12 = 360 months

monthly payment = 525000 * (A/P, 0.75%,360) = 525000 * 0.008046 = 4224.27

b.

Payment left after paying for 2 yrs = 360 - 2 * 12 = 360 - 24 = 336

Principal owed after 2 yrs = 4224.27 * (P/A, 0.75%,336) = 4224.27 * 122.504035 = 517489.97

c.

Interest paid in two yrs = 4224.27 * 24 - (525000 - 517489.97)

= 101382.45 - 7510.04

= 93872.41

d.

New rate = 6.75% = 6.75% / 12 = 0.5625%

t = 20 yrs = 20 * 12 = 240 months

Monthly payment = 517489.97 * (A/P, 0.5625%,240) = 517489.97 * 0.007604 = 3934.81

t= 15 yrs = 15 * 12 = 180 months

Monthly payment = 517489.97 * (A/P, 0.5625%,180) = 517489.97 * 0.008849 = 4579.32