Home Loan Problems Solution for Set 4 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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Julio needs to borrow from the Amarillo National Bank is the principal P.
N is the number of payment periods.
Since Julio has a 28 % deposit, the principal P for the loan is actually the price of the flat minus this deposit amount:
[an error occurred while processing this directive]P = 240000 - 0.01 * 28 * 240000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $172800
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 = 9.0 / 12 / 100
Monthly interest rate = 0.0075
We also need to calculate N, the total number of payments. The repayments happen every month. Julio's loan runs for 15 years, so we can calculate how many months he'll be making payments for:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0075 * 172800 / (1 - (1 + 0.0075)^(-180) )
A = $1752.65
Finally the solution: every month, Julio is going to have to fork out $1752.65 to the Amarillo National Bank to pay off his loan.