Home Loan Problems Solution for Set 9 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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
P is the principal - this is the amount that Zane needs to borrow from the Wilshire State Bank.
N is the number of payment periods.
Since Zane has a 5 % deposit, the principal P for the loan is actually the price of the four bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 300000 - 0.01 * 5 * 300000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $285000
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 = 4.1 / 12 / 100
Monthly interest rate = 0.0034
We also need to calculate N, the total number of payments. Since payments occur every month, and Zane 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 = 0.0034 * 285000 / (1 - (1 + 0.0034)^(-180) )
A = $2122.43
Finally the solution: every month, Zane is going to have to fork out $2122.43 to the Wilshire State Bank to pay off his loan.