Home Loan Problems Solution for Set 5 Question 3
Click here to return to the index page for all Home Loan Problems
Solution to Question 3
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.
The amount that Alden needs to borrow from the PNC Bank is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 19 %, Alden's principal amount will be the cost of the two bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 240000 - 0.01 * 19 * 240000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $194400
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 = 4.4 / 12 / 100
Monthly interest rate = 0.0037
We also need to calculate N, the total number of payments. Since payments occur every month, and Alden 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 = 0.0037 * 194400 / (1 - (1 + 0.0037)^(-120) )
A = $2005.38
Finally the solution: every month, Alden is going to have to fork out $2005.38 to the PNC Bank to pay off his loan.