Home Loan Problems Solution for Set 8 Question 3
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Solution to Question 3
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 Walter needs to borrow from the Nara Bank is the principal P.
N is the number of payment periods.
Since Walter has a 26 % deposit, the principal P for the loan is actually the price of the three bedroom apartment minus this deposit amount:
[an error occurred while processing this directive]P = 570000 - 0.01 * 26 * 570000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $421800
We have a yearly interest rate, but we need the monthly interest rate, which we get by dividing by 12. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 7.8 / 12 / 100
Monthly interest rate = 0.0065
We also need to calculate N, the total number of payments. The repayments happen every month. Walter's loan runs for 10 years, so we can calculate how many months he'll be making payments for:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0065 * 421800 / (1 - (1 + 0.0065)^(-120) )
A = $5073.13
So every month, Walter will have to pay $5073.13 to the Nara Bank.