Home Loan Problems Solution for Set 8 Question 7
Click here to return to the index page for all Home Loan Problems
Solution to Question 7
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.
P is the principal - this is the amount that Roberto needs to borrow from the Woodlands Commercial Bank.
How many payment periods there are is represented by N.
Since Roberto has a 22 % deposit, the principal P for the loan is actually the price of the three bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 210000 - 0.01 * 22 * 210000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $163800
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 = 10.7 / 12 / 100
Monthly interest rate = 0.0089
We also need to calculate N, the total number of payments. The repayments happen every month. Roberto's loan runs for 25 years, so we can calculate how many months he'll be making payments for:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0089 * 163800 / (1 - (1 + 0.0089)^(-300) )
A = $1570.03
So every month, Roberto will have to pay $1570.03 to the Woodlands Commercial Bank.