Home Loan Problems Solution for Set 4 Question 3
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Solution to Question 3
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 Chance needs to borrow from the Mizuho Corporate Bank.
How many payment periods there are is represented by N.
Since Chance has a 17 % deposit, the principal P for the loan is actually the price of the two bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 460000 - 0.01 * 17 * 460000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $381800
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 = 9.7 / 12 / 100
Monthly interest rate = 0.0081
We also need to calculate N, the total number of payments. Since payments occur every month, and Chance has a 20 year loan:
N = 12 * 20
N = 240
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0081 * 381800 / (1 - (1 + 0.0081)^(-240) )
A = $3608.89
Finally the solution: every month, Chance is going to have to fork out $3608.89 to the Mizuho Corporate Bank to pay off his loan.