Home Loan Problems Solution for Set 7 Question 10
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Solution to Question 10
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.
The amount that Phoenix needs to borrow from the Rockland Trust Co. is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 19 %, Phoenix's principal amount will be the cost of the two bedroom house less this deposit amount:
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 = 7.2 / 12 / 100
Monthly interest rate = 0.0060
We also need to calculate N, the total number of payments. The repayments happen every month. Phoenix's loan runs for 20 years, so we can calculate how many months he'll be making payments for:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0060 * 469800 / (1 - (1 + 0.0060)^(-240) )
A = $3698.96
Finally the solution: every month, Phoenix is going to have to fork out $3698.96 to the Rockland Trust Co. to pay off his loan.