Home Loan Problems Solution for Set 7 Question 4
Click here to return to the index page for all Home Loan Problems
Solution to Question 4
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 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 Sheldon needs to borrow from the Manufacturers and Traders Trust.
N is the number of payment periods.
Since Sheldon has a 18 % deposit, the principal P for the loan is actually the price of the house minus this deposit amount:
[an error occurred while processing this directive]P = 440000 - 0.01 * 18 * 440000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $360800
We need to convert the yearly interest rate into something we can use in this question - we need a monthly interest rate, so we need to divide by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 4.6 / 12 / 100
Monthly interest rate = 0.0038
We also need to calculate N, the total number of payments. Since payments occur every month, and Sheldon 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 = 0.0038 * 360800 / (1 - (1 + 0.0038)^(-120) )
A = $3756.72
Finally the solution: every month, Sheldon is going to have to fork out $3756.72 to the Manufacturers and Traders Trust to pay off his loan.