Home Loan Problems Solution for Set 8 Question 4
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Solution to Question 4
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 Jamal needs to borrow from the First Merchants Bank N.A..
How many payment periods there are is represented by N.
Since Jamal has a 12 % deposit, the principal P for the loan is actually the price of the unit minus this deposit amount:
[an error occurred while processing this directive]P = 440000 - 0.01 * 12 * 440000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $387200
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 = 9.5 / 12 / 100
Monthly interest rate = 0.0079
We also need to calculate N, the total number of payments. The repayments happen every month. Jamal'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 = 0.0079 * 387200 / (1 - (1 + 0.0079)^(-180) )
A = $4043.23
So every month, Jamal will have to pay $4043.23 to the First Merchants Bank N.A..