Question

1. Fred was on the seven year plan at the University of South Carolina and racked up $98,000 in student loans, which carry an annual interest rate of 10.8 percent and require monthly payments. His mom has offered to help him pay them off, but she wants to see him become responsible (good luck on that). She has said that if he pays off half of the debt within three years, she will pay the rest. How much would Fred have to pay on his student loan each month so that he had paid off exactly half of it within in three years? (Show your answer as a positive number to the nearest penny)

2. What is the present value of an ordinary annuity of $4,000 per month for 24 years, evaluated at an annual interest rate of 10.7 percent. (Show your answer to two decimals, e.g., 1234.56)

3. After he was injured in a car accident, the insurance company promised to pay Fred $2,000 per month for 5 years. Assuming Fred's opportunity cost is 9.7 percent annually, what is the present value of Fred's settlement?

4. Jane's Dad has offered her a choice for her graduation present when she finishes her studies at College of Charleston: he will either buy a new car, OR he will provide her financial support in the form of $610 per month for the next 3 years. Assuming Jane's opportunity cost for money is 8.5 percent annually, what is the present value of Dad's monthly support checks?

5. A distant cousin named you in their will and has made provisions so that you will receive a single lump sum payment of $77700 in 9 years. What is that worth today, assuming an interest rate of 7.4 percent? (Enter your answer as a positive number)

6. Joe borrowed $15,000 from his uncle, who demanded that Joe repay the loan with interest. Joe's uncle is charging him an annual interest rate of 8.5 percent and wants Joe to pay him at least $250 per month until the loan is repaid. How many months will it take Joe to pay off this loans? (Show your answer to two decimals, e.g., 12.34; fractional months are okay)

7. Fred deposited $11,784 in a savings account that has an Annual Percentage Rate of 8.1 percent interest per year. How much will he have in the account after 10 years? (Show your answer as a positive number)

Answer 1

,1) Payment per month = $98,000 * (10.8%/12) = $882

If has to pay off half of $98,000 it would be $49,000*(10.8%/12)=$504

2) PVA = PMT[(1+i)^n-1/i(1+i)^n]

=$4,000[(1+10.7%^24-1/10.7%(1+10.7%)^24

= $37,383

3)

Year	Settlement	PV factor	PV of settlement
1	$          24,000	0.912	$                21,878
2	$          24,000	0.831	$                19,943
3	$          24,000	0.757	$                18,180
4	$          24,000	0.691	$                16,572
5	$          24,000	0.629	$                15,107
			$                91,680

4)  

Year	Settlement	PV factor	PV of settlement
1	$            7,320	0.922	$                  6,747
2	$            7,320	0.849	$                  6,218
3	$            7,320	0.783	$                  5,731
			$                18,695