Home Loan Problems Solution for Set 10 Question 9
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Solution to Question 9
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 as a decimal, not a percentage, for the period of time at which payments are made.
The amount that Gaven needs to borrow from the Guaranty Bank is the principal P.
N is the number of payment periods.
Since Gaven has a 17 % deposit, the principal P for the loan is actually the price of the two bedroom apartment minus this deposit amount:
P = 150000 - 0.01 * 17 * 150000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $124500
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 = 8.9 / 12 / 100
Monthly interest rate = 0.0074
We also need to calculate N, the total number of payments. The repayments happen every month. Gaven'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 = 0.0074 * 124500 / (1 - (1 + 0.0074)^(-180) )
A = $1255.36
Finally the solution: every month, Gaven is going to have to fork out $1255.36 to the Guaranty Bank to pay off his loan.