Question

Elizabeth wishes to buy a $200,000 house in Lexington, KY. She can afford monthly payments up to $1,100. Thirty-year loans are available at 6% interest compounded monthly. If she can make a $20,000 down payment, can she afford to purchase the house?

Answer 1

Loan amount (P)= 200,000 - 20,000 = 180,000

A = 1100

i = 6% / 12 = 0.5%

n = 12 * 30 = 360

The present value of monthly payment is:

PV = A(P/A, i, n)

= 1100(P/A, 0.5%, 360)

= 1100(166.8)

= $183,480

Since the loan amount ($180,000) is less than the PV of monthly payment, therefore, she can afford to purchase the house.