Home Loan Problems Solution for Set 4 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.
P is the principal - this is the amount that Devonte needs to borrow from the Intrust Bank.
How many payment periods there are is represented by N.
Because the deposit it 19 %, Devonte's principal amount will be the cost of the two bedroom flat less this deposit amount:
[an error occurred while processing this directive]P = 580000 - 0.01 * 19 * 580000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $469800
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 = 10.0 / 12 / 100
Monthly interest rate = 0.0083
We also need to calculate N, the total number of payments. Since payments occur every month, and Devonte has a 25 year loan:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0083 * 469800 / (1 - (1 + 0.0083)^(-300) )
A = $4269.08
Finally the solution: every month, Devonte is going to have to fork out $4269.08 to the Intrust Bank to pay off his loan.