Home Loan Problems Solution for Set 10 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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
The amount that Mateo needs to borrow from the Bank of North Georgia is the principal P.
How many payment periods there are is represented by N.
Since Mateo has a 27 % deposit, the principal P for the loan is actually the price of the four bedroom house minus this deposit amount:
[an error occurred while processing this directive]P = 530000 - 0.01 * 27 * 530000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $386900
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 = 8.5 / 12 / 100
Monthly interest rate = 0.0071
We also need to calculate N, the total number of payments. The repayments happen every month. Mateo's loan runs for 30 years, so we can calculate how many months he'll be making payments for:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0071 * 386900 / (1 - (1 + 0.0071)^(-360) )
A = $2974.93
Finally the solution: every month, Mateo is going to have to fork out $2974.93 to the Bank of North Georgia to pay off his loan.