Question

use x=2 y=0 z=9

You purchase a home for $200,000 and borrow the entire amount from Broadway Bank at an APR of 6% with monthly payments. The maturity of your mortgage equals (30+X) years. a. (8 points) Draw a time line that depicts the cash flows from the mortgage payments i. compute the payment and show your inputs and work. ii. Use negative numbers for outflows and positive for inflows. b. (8 points) Compute the outstanding mortgage amount after you have made (10+Y) years of payments. i. Show this point on the time line, and ii. give the inputs to your computations for full credit. (8 points) c. (9 payments) What is the interest and principal component of your mortgage payment on the next mortgage payment made after (10+Y) years in part (b)? Show your computations.

Answer 1

SOLUTION:-

(a)

The present value of the loan amount PV = 200,000

The monthly interest rate r = 6/12 = 0.5%

The number of periods n = 12 x 31 = 372

The montly payment , PMT = PV / ((1 – (1 / (1 + r) n)) / r) = 1,185.39

Annual payment = PMT x 12 = 14,224.68

(b)

We now have to compute the present value of the loan amount after 12 years.

Number of periods remaining n = (31 - 12) x 12 = 228 months.

r = 0.5%

PMT = 1,185.39

PV = PMT x ((1 – (1 / (1 + r) -n)) / r) = 161,040.26

(c)

To find the interest component, we multiply the principal amount remaining by the monthly interest rate.

Interest = 161,040.26 x 0.005 = 805.2

To find the principal component, we subtract the interest component from the monthly payments.

Principal component = 1,185.39 - 805.2 = 380.19