Question

(d) A property developer has introduced a scheme to help people buy a house. Previously, a person could buy a $250,000 home through a 25% deposit paid once, followed by a mortgage loan for the reminder of the value, repaid over 100 monthly payments at 12% per annum. Today, people can get a mortgage on a $250,000 home with a deposit of only 5%, repaying the remainder of the loan in 100 monthly payments at 24% per annum. Determine the difference in the monthly payments for the two loans as well as the difference in total interest cost of these two loans. (8 marks)

Answer 1

First case

House value = 250000

Deposit = 25% * 250000 = 62500

Loan = 250000 - 62500 = 187500

loan int rate = 12% / 12 = 1% per month

loan tenure = 100 months

Monthly payment = 187500 * (A/P,1%,100) = 187500 * 0.015866 = 2974.875

Total payment = 2974.875 * 100 = 297487.50

Total int payment = 297487.50 - 187500 = 109987.50

Second case

House value = 250000

Deposit = 5% * 250000 = 12500

Loan = 250000 - 12500 = 237500

loan int rate = 24% / 12 = 2% per month

loan tenure = 100 months

Monthly payment = 237500 * (A/P,2%,100) = 237500 * 0.023203 = 5510.7125

Total payment = 5510.7125 * 100 = 551071.25

Total int payment = 551071.25 - 237500 = 313571.25

Diff in monthly payment = 5510.7125 - 2974.875 = 2535.8375 = 2536 (rounding off)

Diff in total interest = 313571.25 - 109987.50 = 203583.75 = 203584 (rounding off)