Home Loan Problems Solution for Set 4 Question 7
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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 Mateo needs to borrow from the Trustmark National Bank.
N is the number of payment periods.
Because the deposit it 12 %, Mateo's principal amount will be the cost of the three bedroom flat less this deposit amount:
[an error occurred while processing this directive]P = 530000 - 0.01 * 12 * 530000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $466400
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 = 8.8 / 12 / 100
Monthly interest rate = 0.0073
We also need to calculate N, the total number of payments. Since payments occur every month, and Mateo has a 10 year loan:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0073 * 466400 / (1 - (1 + 0.0073)^(-120) )
A = $5857.82
Finally the solution: every month, Mateo is going to have to fork out $5857.82 to the Trustmark National Bank to pay off his loan.