A $100,000 loan is to be paid off after 30 years. The annual interest rate is 0.
ID: 2844339 • Letter: A
Question
A $100,000 loan is to be paid off after 30 years. The annual interest rate is 0.09 (9 percent).
(a) What is the interest rate per month (you may leave your answer as a fraction)?
(b) The total amount in the loan after n months is given by P(1+i)n, where P is the starting amount for the loan, i is the monthly interest rate, and n is the total months the loan is being paid off. How much in total will have to be paid off for the loan mentioned above?
(c) Assume you pay a fixed monthly amount D to pay off the loan (the payment is done at the end of the month). After the first month, $D dollars will be paid off of the loan. With the annual interest rate of 0.09 stated above, what is the total paid off after 2 months? What about 3? Determine a general formula for the total paid off after 30 years, which will be in terms of D.
(d) Equate the previous two parts to solve for D.
Explanation / Answer
1(a)
principal=100000
interest rate= 9/12% for 1 month or 9/1200 per year ,
time=30 years,
So, the interest will be=(principal*rate*time)/100=(100000*9*30)/1200=22500
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