Home Loan Problems Solution for Set 4 Question 10
Click here to return to the index page for all Home Loan Problems
Solution to Question 10
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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Talon needs to borrow from the Frost National Bank is the principal P.
N is the number of payment periods.
Since Talon has a 6 % deposit, the principal P for the loan is actually the price of the two bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 360000 - 0.01 * 6 * 360000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $338400
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 = 8.1 / 12 / 100
Monthly interest rate = 0.0067
We also need to calculate N, the total number of payments. The repayments happen every month. Talon's loan runs for 30 years, so we can calculate how many months he'll be making payments for:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0067 * 338400 / (1 - (1 + 0.0067)^(-360) )
A = $2506.69
Finally the solution: every month, Talon is going to have to fork out $2506.69 to the Frost National Bank to pay off his loan.