CHAPTER 2.1: TIME VALUE OF MONEY - EXERCISE Present Value (PV) and Future Value (FV) Problems 1. For liquidity purposes, a client keeps $100,000 in a bank account. The bank quotes a stated annual interest rate of 7%. How much will your client have in his account at the end of one year, assuming no additions or withdrawals, using the following types of compounding: a. Quarterly b. Monthly c. Continuously 2. Jane needs a total of $75,000 in 10 years to pay for the expected college expenses for her granddaughter. If she can earn 8% on her investments, how much of a lump sum does Jane need to invest today? 3. Rick wants to have $35,000 to buy a new truck at the end of four years. His bank has a fouryear CD paying 4% compounded quarterly. How much does Rick need to put into the CD now to reach his goal? 4. When Denise retires in 17 years, she wants to have $400,000. If she can earn 6% on her money, what amount should she invest today to achieve her goal? 5. When Ernie retired, he purchased an annuity that will pay him $6,000 at the beginning of each year for the next 20 years. If Ernie wanted to earn 7% compounded annually on his money, how much should Ernie have paid for the annuity? 6. Tracy won the lottery and has two choices for receiving her winnings. She can receive $10,000 at the end of each year for the next 25 years, or she can take a check for $150,000 today. If Tracy can earn 5% on her money, which option should she take? 7. Justin wants to buy a car. The seller has given him two choices. He can borrow the money to pay for the car and pay $200 at the end of each month for the next 2 1/2 years, or he can pay cash today. If Justin earns 12% compounded monthly on his savings, what’s the most he should pay in cash today? 8. Heather wants to have $20,000 saved up for a down payment on a $100,000 home. She can earn 4% on her savings account. If she wants to buy the home in 3 years, what lump-sum amount does she need to deposit today to achieve her goal? 9. Matthew estimates that he will owe $5,000 in income taxes at the end of one year. If Matthew can earn 12% compounded monthly, how much should he set aside today to have enough saved to pay his taxes? 10. Caitlin wants to have $85,000 available in 6 years to start her own business. If she can earn 9% annually on her money, how much does she need to invest today? 11. Larry wants to buy a bond that will be worth $10,000 at maturity in 7 years. The bond will make $300 semi-annual payments. What’s the maximum price Larry should pay for the bond if his required return is 8%? 12. Julie deposits $250 on the first of each quarter into an investment account, which is growing at 8% compounded quarterly. How much will her account be worth in 10 years? 13. Jamie wants to invest $13,000 for 11 years. If he can earn 8% after tax, how much will his account be worth? 14. Deb has $125,000 in her retirement plan at work. She thinks her portfolio will earn 9% compounded annually in the future. How much will her retirement account be worth in 15 years? 15. Jim is saving up for his son’s college education. He believes he will need a total of $90,000 when his son starts college in 5 years. If Jim invests $8,000 every six months (END) in an account earning 6% compounded semi-annually, will he meet his goal on time? 16. Lila is saving up to start her own part-time business. She currently has $4,000 in her savings account and deposits $1,200 at the end of each 6 months. If she earns 4% compounded semiannually on her savings, how much will her account be worth in 2 years? 17. Keith has $3,000 saved for a down payment on a house. If he adds $500 at the start of every six months to an account earning 6% compounded semi-annually, how much will he have in 4 years? 18. Kevin is the beneficiary of a life insurance policy. He has the choice of receiving a lump sum of $100,000 today, or he can receive $10,000 at the beginning of each year for 15 years. If he can earn 7% on his money, which option should he take? 19. Diane’s portfolio is worth $22,000 today. If she can earn 11% on her investments, how much will Diane’s portfolio be worth in 25 years? 20. Joe owns stock worth $5,000. He invests an additional $600 at the end of every six months in this company. If the value of the stock grows 14% compounded semi-annually, how much will Joe’s account be worth in 5 years? 21. If an investor wants to earn an annual interest rate of 10.76% on a 26 week T-bill with a maturity value of $5,000, how much should the investor pay for the bill? 22. How long will it take for a CD to double, if money earns a simple interest rate of 4.8%? Round up nearest year. 23. Given r=12%, compounded monthly for 8 years; find n (number of months) and i (rate per month). Write i in decimal form 24. (replace 1st) How much should you deposit initially in an account paying 10% compound semiannually in order to have $1,000,000 in 30 years a. Compounded monthly b. Compounded daily c. Continuous compounding 25. Find the APY of each. Which is the better investment: 9% compounded monthly or 9.1% compounded quarterly? 26. Mr Kang borrowed $5200 from his friend to pay for remodeling work on his house. He paid the loan 10 months later with simple interest at 7%. His friend then invested the proceeds in a 5year CD paying 6.3% compounded quarterly. How much will his friend have at the end of the 5 years?
