Home Loan Problems Solution for Set 8 Question 5
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Solution to Question 5
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 Mohammed needs to borrow from the Morgan Stanley Trust is the principal P.
N is the number of payment periods.
Since Mohammed has a 12 % deposit, the principal P for the loan is actually the price of the one bedroom unit minus this deposit amount:
[an error occurred while processing this directive]P = 550000 - 0.01 * 12 * 550000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $484000
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. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 11.5 / 12 / 100
Monthly interest rate = 0.0096
We also need to calculate N, the total number of payments. Since payments occur every month, and Mohammed has a 20 year loan:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0096 * 484000 / (1 - (1 + 0.0096)^(-240) )
A = $5161.52
Finally the solution: every month, Mohammed is going to have to fork out $5161.52 to the Morgan Stanley Trust to pay off his loan.