Home Loan Problems Solution for Set 9 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.
P is the principal - this is the amount that Efrain needs to borrow from the Nevada State Bank.
N is the number of payment periods.
Since Efrain has a 22 % deposit, the principal P for the loan is actually the price of the apartment minus this deposit amount:
[an error occurred while processing this directive]P = 280000 - 0.01 * 22 * 280000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $218400
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 7.3 / 12 / 100
Monthly interest rate = 0.0061
We also need to calculate N, the total number of payments. Since payments occur every month, and Efrain 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 = 0.0061 * 218400 / (1 - (1 + 0.0061)^(-180) )
A = $1999.85
So every month, Efrain will have to pay $1999.85 to the Nevada State Bank.