Home Loan Problems Solution for Set 2 Question 6
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Solution to Question 6
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 Bobby needs to borrow from the Georgian Bank is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 28 %, Bobby's principal amount will be the cost of the one bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 170000 - 0.01 * 28 * 170000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $122400
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 = 7.2 / 12 / 100
Monthly interest rate = 0.0060
We also need to calculate N, the total number of payments. The repayments happen every month. Bobby'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 = 0.0060 * 122400 / (1 - (1 + 0.0060)^(-240) )
A = $963.71
So every month, Bobby will have to pay $963.71 to the Georgian Bank.