Question

Exactly 12 years ago Paul took out a mortgage of $500 000 to buy a house. The loan was taken over 25 years at 12% p.a. with interest compounding monthly and Paul makes monthly repayments. Paul's just won a lottery prize of $400 000. Show that the prize is insufficient to pay out the remaining debt using series

Answer 1

Mortgage = $ 500000, Tenure = 25 years or (25 x 12) = 300 months, Interest Rate = 12 % per annum,

Applicable Monthly Rate = 12/12 = 1 %

Let the monthly repayments be $ N

Therefore, 500000 = N x (1/0.01) x [1-{1/(1.01)^(300)}]

500000 = N x 94.94655

N = 500000 / 94.94655 = $ 5266.12071 ~ $ 5266.12

Remaining Tenure = 25 - 12 = 13 years or (13 x 12) = 156 months

Mortgage Principal Outstanding at the end of 12 years = 5266.12 x (1/0.01) x [1-{1/(1.01)^(156)}] = $ 415091.11

As is observable, the lottery prize of $ 400000 is lesser than the principal outstanding at the end of 12 years and hence is insufficient to pay off the remaining loan