Home Loan Problems Solution for Set 1 Question 1
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Solution to Question 1
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 Keaton needs to borrow from the Southwest Bank is the principal P.
N is the number of payment periods.
Because the deposit it 29 %, Keaton's principal amount will be the cost of the two bedroom house less this deposit amount:
[an error occurred while processing this directive]P = 260000 - 0.01 * 29 * 260000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $184600
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 = 11.1 / 12 / 100
Monthly interest rate = 0.0092
We also need to calculate N, the total number of payments. Since payments occur every month, and Keaton has a 10 year loan:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0092 * 184600 / (1 - (1 + 0.0092)^(-120) )
A = $2553.32
So every month, Keaton will have to pay $2553.32 to the Southwest Bank.