Home Loan Problems Solution for Set 10 Question 4
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Solution to Question 4
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 Kadyn needs to borrow from the Fifth Third Bank.
How many payment periods there are is represented by N.
Because the deposit it 23 %, Kadyn's principal amount will be the cost of the apartment less this deposit amount:
[an error occurred while processing this directive]P = 590000 - 0.01 * 23 * 590000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $454300
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 = 11.8 / 12 / 100
Monthly interest rate = 0.0098
We also need to calculate N, the total number of payments. The repayments happen every month. Kadyn's loan runs for 15 years, so we can calculate how many months he'll be making payments for:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0098 * 454300 / (1 - (1 + 0.0098)^(-180) )
A = $5394.04
Finally the solution: every month, Kadyn is going to have to fork out $5394.04 to the Fifth Third Bank to pay off his loan.