Problem Set: Single Dollar Problems (Solutions Below) 1. If you receive $300.00 in 10 years and the discount rate is 15%, what is the present value? 2. If you want to buy a boat in 6 years that costs $1,000.00 and you now have $600.00, what interest rate would you need? 3. If you put $1,000 in a stock portfolio with a return of 8%, how much would you expect to have in 7 years? 4. How long would you need to wait for $500.00 to double if the interest rate is 10%? 5. If you need $10,000 to pay for your first year of graduate school in 3 years and you get an interest rate of 9%, how much must you invest today? 6. If 6 years ago you invested $500.00 and received an annual interest rate of 4%, how much would you now have? 7. You borrowed $100 from a friend, who said you need to pay back $300 in 5 years, what rate are you being charged? 8. How many years would it take you to have $2,500.00 if you invested $500.00 today at 15%? 9. To have $6000 in 7 years what interest rate would you need if you now had $5,500? 10. If you win a lottery worth $1,000,000 payable in 15 years and the interest rate is 8%, what is this worth today?11. How long does it take for an investment to quadruple in value if the investment yields 6% per year? 12. The average price of a movie ticket at the end of 1988 was $5.50 and the average price of a movie ticket at the end of 1990 was $6.00. At what annual rate did ticket prices grow? 13. If I invest $100 today in an account that earns 10% per year, how much will I have in this account at the end of twenty years if I make no withdrawals? 14. Suppose that I am trying to borrow money from you to finance my business, and I promise to repay you $10,000 in two years. If your opportunity cost of funds is 10%, how much are you willing to lend me? 15. Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest annually at the rate of 9 percent for seven years. How much will Jim have on deposit at the end of seven years? 16. John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 10 percent annually on this investment. The asking price for the lot is $7,000. Should he buy it? 17. An investor can make an investment in a real estate development and receive an expected cash return of $45,000 after six years. Based on a careful study of other investment alternatives, she believes that an 18 percent annual return is a reasonable return to earn on this investment. How much should she pay for it today? 18. Suppose you have the opportunity to make an investment expects to pay investors $75,000 in next eight years. If the cost is $50,000, what return would you receive? 19. Find the values for the following: a. An initial $500 compounded for 1 year at 6 percent. b. An initial $500 compounded for 2 years at 6 percent. c. The present value of $500 due in 1 year at a discount rate of 6 percent.d. The present value of $500 due in 2 years at a discount rate of 6 percent. 20. Which grows to a larger future value, $1000 invested for 2 years at: a) 10 percent each year, b) 5 percent the first year and 15 percent the second year or c) 15 percent the first year and 5 percent the second year? 21. Which grows to a larger future value: i) $2000 invested for 20 years at 10% or ii) $1000 invested for 20 years at 20%? 22. Which is worth more at 14 percent interest, compounded annually: a) $1000 in hand today or b) $2,000 due in 6 years? 23. A 1987 advertisement in the New Yorker solicited offers on a 1967 Mercury Cougar XR7 (Motor Trend's 1967 car of the year) that had been stored undriven in a climate controlled environment for 20 years. If the original owner paid $4000 for this car in 1967, what price would he have to receive in 1987 to obtain a 10 percent annual return on his investment? 24. Vincent Van Gogh sold only one painting during his lifetime, for about $30. A sunflower still life he painted in 1888 sold for $39.85 million in 1988,, more than three times the highest price paid previously for any work of art. If this painting had been purchased for $30 in 1888 and sold in 1988 for $39.85 million, what would have been the annual rate of return? 25. In 1940, your grandmother put $1000 into a special trust to be paid to a future grandchild (you) 60 years later, in the year 2000. How much will this trust be worth in the year 2000 if it has been earning a) 8%? b) 12%. 26. You can either receive a bonus of i) $10,000 in one year or ii) $20,000 in five years. Which is better if the discount rate is a) 10%? b) 20%? 27. At an interest rate of 10%, what is present value of $1m to be received in: a. 10 years b. 50 years c. 100 yearsd. 150 years 28. You are a CEO of a firm worth $10 million and you plan to stay until the firm has tripled in value. How long do you expect to be the CEO, if the expected growth rate is 15%? 29. A friend boasts that his investment doubled in 4 years. What was his annual return? 30. Your parents are astonished when they find out that you had to spend $700 on books and supplies, since it would only have cost them $200. If the inflation on these items was 5%, how long ago did your parents go to college?Solutions 1. N = 10; I/Y = 15; PV = $74.16; FV = -300 2. N = 6; I/Y = 8.89%; PV = 600; FV = -1,000 3. N = 7; I/Y = 8; PV = -1,000; FV = $1,713.82 4. N = 7.27; I/Y = 10; PV = 500; FV = -1,000  7.27 = 7 years + 0.27 years, 12 x 0.27 = 3.24 ≈ 3  7 years 3 months 5. N = 3; I/Y = 9; PV = $7,721.83; FV = -10,000 6. N = 6; I/Y = 4; PV = -500; FV = $632.66 7. N = 5; I/Y = 24.57%; PV = 100; FV = -300 8. N = 11.52; I/Y = 15; PV = 500; FV = -2,500  11.52 = 11 years + 0.52 years, 12 x 0.52 = 6.24 ≈ 6  11 years 6 months 9. N = 7; I/Y = 1.25%; PV = 5,500; FV = -6,000 10. N = 15; I/Y = 8; PV …