Home Loan Problems Solution for Set 4 Question 6
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Solution to Question 6
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 Freddy needs to borrow from the Bank of America Oregon.
How many payment periods there are is represented by N.
Because the deposit it 26 %, Freddy's principal amount will be the cost of the one bedroom apartment less this deposit amount:
[an error occurred while processing this directive]P = 280000 - 0.01 * 26 * 280000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $207200
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 = 9.1 / 12 / 100
Monthly interest rate = 0.0076
We also need to calculate N, the total number of payments. The repayments happen every month. Freddy's loan runs for 20 years, so we can calculate how many months he'll be making payments for:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0076 * 207200 / (1 - (1 + 0.0076)^(-240) )
A = $1877.57
Finally the solution: every month, Freddy is going to have to fork out $1877.57 to the Bank of America Oregon to pay off his loan.