Home Loan Problems Solution for Set 1 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 Carson needs to borrow from the Enterprise Bank & Trust.
N is the number of payment periods.
Because the deposit it 13 %, Carson's principal amount will be the cost of the three bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 190000 - 0.01 * 13 * 190000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $165300
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 4.8 / 12 / 100
Monthly interest rate = 0.0040
We also need to calculate N, the total number of payments. Since payments occur every month, and Carson has a 30 year loan:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0040 * 165300 / (1 - (1 + 0.0040)^(-360) )
A = $867.28
Finally the solution: every month, Carson is going to have to fork out $867.28 to the Enterprise Bank & Trust to pay off his loan.