Home Loan Problems Solution for Set 10 Question 1
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Solution to Question 1
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 Gael needs to borrow from the International Bank of Commerce.
N is the number of payment periods.
Since Gael has a 11 % deposit, the principal P for the loan is actually the price of the two bedroom apartment minus this deposit amount:
[an error occurred while processing this directive]P = 350000 - 0.01 * 11 * 350000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $311500
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 = 7.1 / 12 / 100
Monthly interest rate = 0.0059
We also need to calculate N, the total number of payments. Since payments occur every month, and Gael has a 20 year loan:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0059 * 311500 / (1 - (1 + 0.0059)^(-240) )
A = $2433.78
Finally the solution: every month, Gael is going to have to fork out $2433.78 to the International Bank of Commerce to pay off his loan.