Home Loan Problems Solution for Set 4 Question 2
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Solution to Question 2
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 Ian needs to borrow from the Republic Bank & Trust Co. is the principal P.
N is the number of payment periods.
Since Ian has a 16 % deposit, the principal P for the loan is actually the price of the three bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 390000 - 0.01 * 16 * 390000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $327600
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 = 4.9 / 12 / 100
Monthly interest rate = 0.0041
We also need to calculate N, the total number of payments. The repayments happen every month. Ian'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 = 0.0041 * 327600 / (1 - (1 + 0.0041)^(-360) )
A = $1738.67
Finally the solution: every month, Ian is going to have to fork out $1738.67 to the Republic Bank & Trust Co. to pay off his loan.