Home Loan Problems Solution for Set 8 Question 9
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Solution to Question 9
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 Zachary needs to borrow from the Mechanics Bank.
N is the number of payment periods.
Since Zachary has a 9 % deposit, the principal P for the loan is actually the price of the flat minus this deposit amount:
[an error occurred while processing this directive]P = 450000 - 0.01 * 9 * 450000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $409500
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 = 9.1 / 12 / 100
Monthly interest rate = 0.0076
We also need to calculate N, the total number of payments. Since payments occur every month, and Zachary 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 = 0.0076 * 409500 / (1 - (1 + 0.0076)^(-180) )
A = $4177.81
Finally the solution: every month, Zachary is going to have to fork out $4177.81 to the Mechanics Bank to pay off his loan.