Home Loan Problems Solution for Set 5 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 Donavan needs to borrow from the Pacific National Bank.
How many payment periods there are is represented by N.
Because the deposit it 24 %, Donavan's principal amount will be the cost of the three bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 500000 - 0.01 * 24 * 500000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $380000
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. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 2.7 / 12 / 100
Monthly interest rate = 0.0023
We also need to calculate N, the total number of payments. Since payments occur every month, and Donavan 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 = 0.0023 * 380000 / (1 - (1 + 0.0023)^(-360) )
A = $1541.29
Finally the solution: every month, Donavan is going to have to fork out $1541.29 to the Pacific National Bank to pay off his loan.