Home Loan Problems Solution for Set 9 Question 6
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Solution to Question 6
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.
P is the principal - this is the amount that Tristan needs to borrow from the M & I Bank FSB.
How many payment periods there are is represented by N.
Since Tristan has a 30 % deposit, the principal P for the loan is actually the price of the one bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 590000 - 0.01 * 30 * 590000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $413000
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 = 4.9 / 12 / 100
Monthly interest rate = 0.0041
We also need to calculate N, the total number of payments. Since payments occur every month, and Tristan 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 = 0.0041 * 413000 / (1 - (1 + 0.0041)^(-360) )
A = $2191.91
Finally the solution: every month, Tristan is going to have to fork out $2191.91 to the M & I Bank FSB to pay off his loan.