Home Loan Problems Solution for Set 3 Question 9
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Solution to Question 9
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 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 Ronald needs to borrow from the Tri Counties Bank.
N is the number of payment periods.
Because the deposit it 7 %, Ronald's principal amount will be the cost of the flat less this deposit amount:
[an error occurred while processing this directive]P = 500000 - 0.01 * 7 * 500000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $465000
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 = 6.6 / 12 / 100
Monthly interest rate = 0.0055
We also need to calculate N, the total number of payments. Since payments occur every month, and Ronald has a 25 year loan:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0055 * 465000 / (1 - (1 + 0.0055)^(-300) )
A = $3168.84
Finally the solution: every month, Ronald is going to have to fork out $3168.84 to the Tri Counties Bank to pay off his loan.