Home Loan Problems Solution for Set 10 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.
P is the principal - this is the amount that Neil needs to borrow from the Integra Bank N.A..
How many payment periods there are is represented by N.
Because the deposit it 15 %, Neil's principal amount will be the cost of the three bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 170000 - 0.01 * 15 * 170000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $144500
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. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 2.7 / 12 / 100
Monthly interest rate = 0.0023
We also need to calculate N, the total number of payments. The repayments happen every month. Neil's loan runs for 25 years, so we can calculate how many months he'll be making payments for:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0023 * 144500 / (1 - (1 + 0.0023)^(-300) )
A = $662.91
Finally the solution: every month, Neil is going to have to fork out $662.91 to the Integra Bank N.A. to pay off his loan.