Question

What happens to the present value of an annuity if the discount rate is increased? Why? What about its future value? 2. Assume an athlete signs ten year contracts that pay out a total of $25 million over the life of the contracts. One contract will pay $4.8 million per year over 5 years and 2.4 million the last 5 years. Another contract will pay $4 million per year over 10 years. The last and third contract option is a lump sum payment of $25 million. Which should the athlete choose if the discount rate is 10%? 3. Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they do not save any additional funds? 4. What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year? If this was an annuity due, what would its future value be? 5. An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5 and $500 at the end of Year 6. If the interest rate is 8%, what is the present value of these cash flows? What is the investment’s future value? 6. You want to buy a car, and a local bank will lend you $20,000. The loan will be paid over 5 years and the annual percentage rate will be 12% with interest paid monthly. What will be the monthly loan payment?

Answer 1

3. Your parents will retire in 18 years. They currently have $250,000, and they think they will need $1,000,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they do not save any additional funds?
=(1000000/250000)^(1/18)-1=8.006%

4. What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year?
=300/7%*(1.07^5-1)=$1,725.22

If this was an annuity due, what would its future value be?
=300/7%*(1.07^5-1)*1.07=$1,845.99

5. An investment will pay $100 at the end of each of the next 3 years, $200 at the end of Year 4, $300 at the end of Year 5 and $500 at the end of Year 6. If the interest rate is 8%, what is the present value of these cash flows?
Present value=100/1.08+100/1.08^2+100/1.08^3+200/1.08^4+300/1.08^5+500/1.08^6=$923.98

What is the investment’s future value?
Future Value=923.98*1.08^6=$1,466.24

6. You want to buy a car, and a local bank will lend you $20,000. The loan will be paid over 5 years and the annual percentage rate will be 12% with interest paid monthly. What will be the monthly loan payment?

=20000*12%/12*1/(1-1/(1+12%/12)^(12*5))=$444.89

P.S.: I am not allowed to answer more than 4 questions