Home Loan Problems Solution for Set 3 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 as a decimal, not a percentage, for the period of time at which payments are made.
P is the principal - this is the amount that Lewis needs to borrow from the Corus Bank.
How many payment periods there are is represented by N.
Because the deposit it 16 %, Lewis's principal amount will be the cost of the one bedroom flat less this deposit amount:
[an error occurred while processing this directive]P = 360000 - 0.01 * 16 * 360000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $302400
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 = 7.7 / 12 / 100
Monthly interest rate = 0.0064
We also need to calculate N, the total number of payments. Since payments occur every month, and Lewis has a 15 year loan:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0064 * 302400 / (1 - (1 + 0.0064)^(-180) )
A = $2837.76
Finally the solution: every month, Lewis is going to have to fork out $2837.76 to the Corus Bank to pay off his loan.