Home Loan Problems Solution for Set 9 Question 1
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Solution to Question 1
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.
P is the principal - this is the amount that Abdullah needs to borrow from the People's United Bank.
N is the number of payment periods.
Since Abdullah has a 14 % deposit, the principal P for the loan is actually the price of the granny flat minus this deposit amount:
P = 380000 - 0.01 * 14 * 380000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $326800
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. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 5.8 / 12 / 100
Monthly interest rate = 0.0048
We also need to calculate N, the total number of payments. The repayments happen every month. Abdullah's loan runs for 15 years, so we can calculate how many months he'll be making payments for:
N = 12 * 15
N = 180
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0048 * 326800 / (1 - (1 + 0.0048)^(-180) )
A = $2722.54
So every month, Abdullah will have to pay $2722.54 to the People's United Bank.