Home Loan Problems Solution for Set 8 Question 1
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Solution to Question 1
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.
P is the principal - this is the amount that Andy needs to borrow from the First Commercial Bank.
N is the number of payment periods.
Since Andy has a 30 % deposit, the principal P for the loan is actually the price of the three bedroom flat minus this deposit amount:
[an error occurred while processing this directive]P = 560000 - 0.01 * 30 * 560000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $392000
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 = 2.1 / 12 / 100
Monthly interest rate = 0.0018
We also need to calculate N, the total number of payments. Since payments occur every month, and Andy 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 = 0.0018 * 392000 / (1 - (1 + 0.0018)^(-240) )
A = $2001.69
So every month, Andy will have to pay $2001.69 to the First Commercial Bank.