Home Loan Problems Solution for Set 8 Question 2
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Solution to Question 2
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 Eddie needs to borrow from the Bank Hapoalim B.M..
N is the number of payment periods.
Because the deposit it 16 %, Eddie's principal amount will be the cost of the one bedroom house less this deposit amount:
[an error occurred while processing this directive]P = 580000 - 0.01 * 16 * 580000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $487200
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 = 10.1 / 12 / 100
Monthly interest rate = 0.0084
We also need to calculate N, the total number of payments. Since payments occur every month, and Eddie has a 15 year loan:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0084 * 487200 / (1 - (1 + 0.0084)^(-180) )
A = $5265.33
Finally the solution: every month, Eddie is going to have to fork out $5265.33 to the Bank Hapoalim B.M. to pay off his loan.