Home Loan Problems Solution for Set 10 Question 6
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Solution to Question 6
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.
The amount that Jaime needs to borrow from the Columbus Bank and Trust Co. is the principal P.
N is the number of payment periods.
Because the deposit it 6 %, Jaime's principal amount will be the cost of the flat less this deposit amount:
[an error occurred while processing this directive]P = 240000 - 0.01 * 6 * 240000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $225600
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 = 2.9 / 12 / 100
Monthly interest rate = 0.0024
We also need to calculate N, the total number of payments. The repayments happen every month. Jaime'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 = 0.0024 * 225600 / (1 - (1 + 0.0024)^(-300) )
A = $1058.14
Finally the solution: every month, Jaime is going to have to fork out $1058.14 to the Columbus Bank and Trust Co. to pay off his loan.