Home Loan Problems Solution for Set 8 Question 8
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Solution to Question 8
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 expressed as a decimal (NOT A PERCENTAGE!), for the period of time over which payments are made.
P is the principal - this is the amount that Shamar needs to borrow from the Citibank.
N is the number of payment periods.
Because the deposit it 11 %, Shamar's principal amount will be the cost of the house less this deposit amount:
[an error occurred while processing this directive]P = 210000 - 0.01 * 11 * 210000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $186900
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 = 10.0 / 12 / 100
Monthly interest rate = 0.0083
We also need to calculate N, the total number of payments. Since payments occur every month, and Shamar has a 30 year loan:
N = 12 * 30
N = 360
Armed with this information we can now fill in the numbers and then calculate the answer:
A = 0.0083 * 186900 / (1 - (1 + 0.0083)^(-360) )
A = $1640.18
Finally the solution: every month, Shamar is going to have to fork out $1640.18 to the Citibank to pay off his loan.