Question

You plan to purchase an $110,000 house using a 15-year mortgage obtained from your local bank. The mortgage rate offered to you is 4.25 percent. You will make a down payment of 12 percent of the purchase price.

a. Calculate your monthly payments on this mortgage.
b. Calculate the amount of interest and, separately, principal paid in the 100th payment.
c. Calculate the amount of interest and, separately, principal paid in the 115th payment.
d. Calculate the amount of interest paid over the life of this mortgage.
  

Answer 1

a) Down payment = $110000 *12% = $13200

Amount financed by mortgage =$110000 - $13200 = $96800

Monthly rate =4.25%/12 =0.003542

No of months =15*12 =180

So, Monthly mortgage payment (A) is given by

A/0.003542*(1-1/1.003542^180) = 96800

=> 132.9295*A =96800

=> A = $728.21

b) Principal remaining after 99th payment (81 payments remaining)

= 728.21/0.003542*(1-1/1.003542^81)

=$51200.00

So, interest paid in 100th payment = $51200*0.003542 = $181.33

Principal paid in 100th payment = $728.21- $181.33 = $546.87

c)

Principal remaining after 114th payment (66 payments remaining)

= 728.21/0.003542*(1-1/1.003542^66)

=$42790.39

So, interest paid in 115th payment = $42790.39*0.003542 = $151.55

Principal paid in 115th payment = $728.21- $151.55 = $576.66

d) Total Amount paid over the life of mortgage = $728.21*180 = $131076.99

So, Total Interest paid = $131076.99- $96800 = $34276.99