Home Loan Problems Solution for Set 6 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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Zaire needs to borrow from the First Federal Bank of the Midwest is the principal P.
N is the number of payment periods.
Since Zaire has a 5 % deposit, the principal P for the loan is actually the price of the three bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 560000 - 0.01 * 5 * 560000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $532000
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 = 9.7 / 12 / 100
Monthly interest rate = 0.0081
We also need to calculate N, the total number of payments. Since payments occur every month, and Zaire 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 = 0.0081 * 532000 / (1 - (1 + 0.0081)^(-240) )
A = $5028.62
Finally the solution: every month, Zaire is going to have to fork out $5028.62 to the First Federal Bank of the Midwest to pay off his loan.