Home Loan Problems Solution for Set 5 Question 7
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Solution to Question 7
The equation you need to use is as follows:
A = i * P / (1 - (1 + i)^(-N) )
A is the payment Amount each month.
i is the interest rate as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Keon needs to borrow from the Middlesex Savings Bank is the principal P.
N is the number of payment periods.
Because the deposit it 26 %, Keon's principal amount will be the cost of the one bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 450000 - 0.01 * 26 * 450000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $333000
We need to convert the yearly interest rate into something we can use in this question - we need a monthly interest rate, so we need to divide by 12. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 5.7 / 12 / 100
Monthly interest rate = 0.0048
We also need to calculate N, the total number of payments. The repayments happen every month. Keon's loan runs for 10 years, so we can calculate how many months he'll be making payments for:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0048 * 333000 / (1 - (1 + 0.0048)^(-120) )
A = $3647.01
Finally the solution: every month, Keon is going to have to fork out $3647.01 to the Middlesex Savings Bank to pay off his loan.