Home Loan Problems Solution for Set 1 Question 9
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Solution to Question 9
For this type of question, you need this following equation:
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 Francisco needs to borrow from the First National Bank is the principal P.
N is the number of payment periods.
Because the deposit it 27 %, Francisco's principal amount will be the cost of the one bedroom flat less this deposit amount:
P = 520000 - 0.01 * 27 * 520000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $379600
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into 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. Francisco's loan runs for 10 years, so we can calculate how many months he'll be making payments for:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0089 * 379600 / (1 - (1 + 0.0089)^(-120) )
A = $5164.75
Finally the solution: every month, Francisco is going to have to fork out $5164.75 to the First National Bank to pay off his loan.