Home Loan Problems Solution for Set 5 Question 1
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Solution to Question 1
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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
The amount that Jamie needs to borrow from the Tri Counties Bank is the principal P.
N is the number of payment periods.
Since Jamie has a 28 % deposit, the principal P for the loan is actually the price of the three bedroom unit minus this deposit amount:
P = 280000 - 0.01 * 28 * 280000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $201600
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 8.1 / 12 / 100
Monthly interest rate = 0.0067
We also need to calculate N, the total number of payments. The repayments happen every month. Jamie's loan runs for 30 years, so we can calculate how many months he'll be making payments for:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0067 * 201600 / (1 - (1 + 0.0067)^(-360) )
A = $1493.35
So every month, Jamie will have to pay $1493.35 to the Tri Counties Bank.