Home Loan Problems Solution for Set 9 Question 9
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Solution to Question 9
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 Atticus needs to borrow from the U.S. Bank N.A. ND.
N is the number of payment periods.
Because the deposit it 20 %, Atticus's principal amount will be the cost of the one bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 490000 - 0.01 * 20 * 490000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $392000
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 = 10.4 / 12 / 100
Monthly interest rate = 0.0087
We also need to calculate N, the total number of payments. Since payments occur every month, and Atticus has a 20 year loan:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0087 * 392000 / (1 - (1 + 0.0087)^(-240) )
A = $3887.36
So every month, Atticus will have to pay $3887.36 to the U.S. Bank N.A. ND.