Home Loan Problems Solution for Set 1 Question 3
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Solution to Question 3
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 Javen needs to borrow from the UMB Bank.
N is the number of payment periods.
Since Javen has a 7 % deposit, the principal P for the loan is actually the price of the one bedroom unit minus this deposit amount:
[an error occurred while processing this directive]P = 540000 - 0.01 * 7 * 540000 (we need the 0.01 to convert the deposit percentage into a decimal)
P = $502200
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. We also need to divide the percentage rate by 100 to turn it into a decimal rate:
Monthly interest rate = 3.8 / 12 / 100
Monthly interest rate = 0.0032
We also need to calculate N, the total number of payments. Since payments occur every month, and Javen 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 = 0.0032 * 502200 / (1 - (1 + 0.0032)^(-360) )
A = $2340.03
So every month, Javen will have to pay $2340.03 to the UMB Bank.