Home Loan Problems Solution for Set 9 Question 4
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Solution to Question 4
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 Alden needs to borrow from the Provident Bank.
How many payment periods there are is represented by N.
Because the deposit it 20 %, Alden's principal amount will be the cost of the two bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 270000 - 0.01 * 20 * 270000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $216000
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 = 5.2 / 12 / 100
Monthly interest rate = 0.0043
We also need to calculate N, the total number of payments. The repayments happen every month. Alden's loan runs for 30 years, so we can calculate how many months he'll be making payments for:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0043 * 216000 / (1 - (1 + 0.0043)^(-360) )
A = $1186.07
So every month, Alden will have to pay $1186.07 to the Provident Bank.