Home Loan Problems Solution for Set 10 Question 7
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Solution to Question 7
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 Tyrell needs to borrow from the Northern Trust Co..
N is the number of payment periods.
Because the deposit it 9 %, Tyrell's principal amount will be the cost of the two bedroom unit less this deposit amount:
[an error occurred while processing this directive]P = 390000 - 0.01 * 9 * 390000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $354900
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 3.4 / 12 / 100
Monthly interest rate = 0.0028
We also need to calculate N, the total number of payments. The repayments happen every month. Tyrell'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 = 0.0028 * 354900 / (1 - (1 + 0.0028)^(-120) )
A = $3492.82
Finally the solution: every month, Tyrell is going to have to fork out $3492.82 to the Northern Trust Co. to pay off his loan.