Home Loan Problems Solution for Set 1 Question 10
Click here to return to the index page for all Home Loan Problems
Solution to Question 10
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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Jairo needs to borrow from the Westernbank Puerto Rico is the principal P.
N is the number of payment periods.
Because the deposit it 23 %, Jairo's principal amount will be the cost of the three bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 160000 - 0.01 * 23 * 160000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $123200
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 = 7.7 / 12 / 100
Monthly interest rate = 0.0064
We also need to calculate N, the total number of payments. Since payments occur every month, and Jairo 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 = 0.0064 * 123200 / (1 - (1 + 0.0064)^(-180) )
A = $1156.12
Finally the solution: every month, Jairo is going to have to fork out $1156.12 to the Westernbank Puerto Rico to pay off his loan.