Home Loan Problems Solution for Set 1 Question 7
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Solution to Question 7
For this type of question, you need this following equation:
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 Conner needs to borrow from the SCBT N.A. is the principal P.
How many payment periods there are is represented by N.
Since Conner has a 22 % deposit, the principal P for the loan is actually the price of the three bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 430000 - 0.01 * 22 * 430000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $335400
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 = 4.6 / 12 / 100
Monthly interest rate = 0.0038
We also need to calculate N, the total number of payments. The repayments happen every month. Conner'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 = 0.0038 * 335400 / (1 - (1 + 0.0038)^(-120) )
A = $3492.25
Finally the solution: every month, Conner is going to have to fork out $3492.25 to the SCBT N.A. to pay off his loan.