Question

Suppose that you are considering a conventional, fixed-rate 30-year mortgage loan for $100,000. The lender quotes an APR of 3.28%, compounded monthly; mortgage payments would be monthly, beginning one month after the closing on your home purchase. After 10 years of payments, what is the balance outstanding on your loan?

Do not round at intermediate steps in your calculation. Round your answer to the nearest penny. Do not type the $ symbol.

Answer 1

Monthly interest rate = 3.28%/12 = 0.2733%

No. of payments = 30*12 =360

Present value of mortgage payments (P) = Loan Amount = $100,000

=> P/1.002733 + P/1.002733^2 + ... + P/1.002733^360 = 100000

=> P/0.002733 * (1-1/1.002733^360) = 100000

=>P*228.9091 = 100000

=> P = $436.85

Balance outstanding is the difference between the future value of Loan and Mortgage payments

Future Value of Loan after 10 years = 100000* (1+0.002733)^120 = $138756.7964

Future value of Mortgage payments after 10 years = P/r* ((1+r)^n-1)

= 436.85/0.002733 *(1.002733^120-1)

=138756.7964

So, Balance Outstanding after 10 years = 138756.7964- 138756.7964 = 76813.81