Home Loan Problems Solution for Set 6 Question 7
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Solution to Question 7
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 Gannon needs to borrow from the First Federal Bank of Calif. is the principal P.
How many payment periods there are is represented by N.
Since Gannon has a 7 % deposit, the principal P for the loan is actually the price of the one bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 460000 - 0.01 * 7 * 460000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $427800
We need to convert the yearly interest rate into something we can use in this question - we need a monthly interest rate, so we need to divide by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 8.9 / 12 / 100
Monthly interest rate = 0.0074
We also need to calculate N, the total number of payments. Since payments occur every month, and Gannon has a 15 year loan:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0074 * 427800 / (1 - (1 + 0.0074)^(-180) )
A = $4313.60
Finally the solution: every month, Gannon is going to have to fork out $4313.60 to the First Federal Bank of Calif. to pay off his loan.