Home Loan Problems Solution for Set 6 Question 3
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Solution to Question 3
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 Dexter needs to borrow from the State Bank & Trust is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 9 %, Dexter's principal amount will be the cost of the one bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 410000 - 0.01 * 9 * 410000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $373100
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 4.5 / 12 / 100
Monthly interest rate = 0.0037
We also need to calculate N, the total number of payments. The repayments happen every month. Dexter's loan runs for 20 years, so we can calculate how many months he'll be making payments for:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0037 * 373100 / (1 - (1 + 0.0037)^(-240) )
A = $2360.43
So every month, Dexter will have to pay $2360.43 to the State Bank & Trust.