Home Loan Problems Solution for Set 5 Question 8
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Solution to Question 8
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.
P is the principal - this is the amount that Rylee needs to borrow from the Sterling National Bank.
How many payment periods there are is represented by N.
Because the deposit it 6 %, Rylee's principal amount will be the cost of the two bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 460000 - 0.01 * 6 * 460000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $432400
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 = 3.6 / 12 / 100
Monthly interest rate = 0.0030
We also need to calculate N, the total number of payments. Since payments occur every month, and Rylee 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 = 0.0030 * 432400 / (1 - (1 + 0.0030)^(-180) )
A = $3112.41
So every month, Rylee will have to pay $3112.41 to the Sterling National Bank.