Home Loan Problems Solution for Set 5 Question 4
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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 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 Ariel needs to borrow from the Keybank N.A..
How many payment periods there are is represented by N.
Since Ariel has a 25 % deposit, the principal P for the loan is actually the price of the three bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 320000 - 0.01 * 25 * 320000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $240000
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 = 6.4 / 12 / 100
Monthly interest rate = 0.0053
We also need to calculate N, the total number of payments. The repayments happen every month. Ariel's loan runs for 10 years, so we can calculate how many months he'll be making payments for:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0053 * 240000 / (1 - (1 + 0.0053)^(-120) )
A = $2712.97
So every month, Ariel will have to pay $2712.97 to the Keybank N.A..