Home Loan Problems Solution for Set 5 Question 9
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Solution to Question 9
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 Mohammed needs to borrow from the Sterling Savings Bank is the principal P.
How many payment periods there are is represented by N.
Because the deposit it 11 %, Mohammed's principal amount will be the cost of the three bedroom flat less this deposit amount:
[an error occurred while processing this directive]P = 260000 - 0.01 * 11 * 260000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $231400
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. The percentage rate needs to be divided by 100 to convert it to a decimal rate:
Monthly interest rate = 11.4 / 12 / 100
Monthly interest rate = 0.0095
We also need to calculate N, the total number of payments. The repayments happen every month. Mohammed'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 = 0.0095 * 231400 / (1 - (1 + 0.0095)^(-360) )
A = $2273.89
So every month, Mohammed will have to pay $2273.89 to the Sterling Savings Bank.