Home Loan Problems Solution for Set 1 Question 4
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Solution to Question 4
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 Chaim needs to borrow from the Center Bank is the principal P.
How many payment periods there are is represented by N.
Since Chaim has a 24 % deposit, the principal P for the loan is actually the price of the three bedroom unit minus this deposit amount:
[an error occurred while processing this directive]P = 510000 - 0.01 * 24 * 510000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $387600
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 = 6.0 / 12 / 100
Monthly interest rate = 0.0050
We also need to calculate N, the total number of payments. The repayments happen every month. Chaim's loan runs for 25 years, so we can calculate how many months he'll be making payments for:
N = 12 * 25
N = 300
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0050 * 387600 / (1 - (1 + 0.0050)^(-300) )
A = $2497.31
Finally the solution: every month, Chaim is going to have to fork out $2497.31 to the Center Bank to pay off his loan.