Home Loan Problems Solution for Set 2 Question 10
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Solution to Question 10
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 Rhys needs to borrow from the Mizuho Corporate Bank is the principal P.
N is the number of payment periods.
Since Rhys has a 15 % deposit, the principal P for the loan is actually the price of the two bedroom house minus this deposit amount:
P = 540000 - 0.01 * 15 * 540000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $459000
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 = 4.8 / 12 / 100
Monthly interest rate = 0.0040
We also need to calculate N, the total number of payments. Since payments occur every month, and Rhys has a 10 year loan:
N = 12 * 10
N = 120
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0040 * 459000 / (1 - (1 + 0.0040)^(-120) )
A = $4823.71
Finally the solution: every month, Rhys is going to have to fork out $4823.71 to the Mizuho Corporate Bank to pay off his loan.