Home Loan Problems Solution for Set 2 Question 4
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Solution to Question 4
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.
The amount that Riley needs to borrow from the Home S&L Company is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 10 %, Riley's principal amount will be the cost of the one bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 270000 - 0.01 * 10 * 270000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $243000
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 = 2.4 / 12 / 100
Monthly interest rate = 0.0020
We also need to calculate N, the total number of payments. Since payments occur every month, and Riley has a 10 year loan:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0020 * 243000 / (1 - (1 + 0.0020)^(-120) )
A = $2279.75
So every month, Riley will have to pay $2279.75 to the Home S&L Company.