Home Loan Problems Solution for Set 5 Question 5
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Solution to Question 5
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 Bruno needs to borrow from the Valley National Bank is the principal P.
How many payment periods there are is represented by N.
Since Bruno has a 20 % deposit, the principal P for the loan is actually the price of the house minus this deposit amount:
[an error occurred while processing this directive]P = 520000 - 0.01 * 20 * 520000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $416000
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 = 8.1 / 12 / 100
Monthly interest rate = 0.0067
We also need to calculate N, the total number of payments. The repayments happen every month. Bruno's loan runs for 20 years, so we can calculate how many months he'll be making payments for:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0067 * 416000 / (1 - (1 + 0.0067)^(-240) )
A = $3505.53
Finally the solution: every month, Bruno is going to have to fork out $3505.53 to the Valley National Bank to pay off his loan.