Question

20pts) 5. William would like to purchase a house worth $350,000. He can afford to make a down payment of $50,000 and needs to take out a mortgage. The bank offers him a 35-year mortgage with monthly payments. The interest rate is 7% APR with semi-annual compounding. a) What will be his monthly payments? b) He can only afford to make payments of $ 1500 per month. The bank agrees to this provided he pays the remaining amount in a lump sum fashion at the end of 35 years. How much will he have to pay lump sum at the end of 35 years? Draw the time line.

Answer 1

(a)

House Worth = $ 350000, Down Payment = $ 50000, Mortgage Value = 350000 - 50000 = $ 300000

APR = 7%, Compounding Frequency: Semi-Annual

Applicable Monthly Interest Rate = [1+(0.07/2)]^(2/12) - 1 = 0.00575 %

Mortgage Tenure = 35 years or (35 x 2 ) = 70 half-years

Let the monthly repayments be $ P

Therefore, 300000 = P x (1/0.00575) x [1-{1/(1.00575)^(70)}]

300000 = P x 57.49252

P = 300000 / 57.49252 = $ 5218.07

(b) Maximum Monthly Payments = $ 1500 and let the required lumpsum payment be $ K

Therefore, 300000 = 1500 x (1/0.00575) x [1-{1/(1.00575)^(70)}] + K / (1.00575)^(70)

300000 = 86238.78 + K x 0.66941574

K = (300000 - 86238.78) / 0.66941574 = $ 319325.0584 ~ $ 319325.06