Home Loan Problems Solution for Set 4 Question 4
Click here to return to the index page for all Home Loan Problems
Solution to Question 4
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 Holden needs to borrow from the State Street Bank and Trust Co..
How many payment periods there are is represented by N.
Because the deposit it 26 %, Holden's principal amount will be the cost of the house less this deposit amount:
[an error occurred while processing this directive]P = 280000 - 0.01 * 26 * 280000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $207200
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 = 11.0 / 12 / 100
Monthly interest rate = 0.0092
We also need to calculate N, the total number of payments. Since payments occur every month, and Holden has a 30 year loan:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0092 * 207200 / (1 - (1 + 0.0092)^(-360) )
A = $1973.21
So every month, Holden will have to pay $1973.21 to the State Street Bank and Trust Co..