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Exercises on Time Value of Money

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**1. **BUS 342 - Muge Tiryakioglu Exercises on Time Value of Money

**2. **BUS 342 - Muge Tiryakioglu 1. Calculating Future Value Your wealthy uncle established a $1,000 bank account for you when you were born. For the first 8 years of your life, the interest rate earned on the account was 8 percent. Since then, rates have only been 6 percent. Now you are 21 years old and ready to cash in. How much is in your account?

**3. **BUS 342 - Muge Tiryakioglu 2. Calculating Annuity Values You have just won the $28,000,000 superbowl lotto. The winnings are paid in 20 equal annual installments. The first payment is tomorrow. You have been contacted by a financial service company that is willing to trade an immediate single lump sum for your payments. What lump sum would be acceptable to you if the average interest rate is 8%?

**4. **BUS 342 - Muge Tiryakioglu 3. Calculating Loan Payments You want to buy a state-of the-art laptop computer that sells for $1,850. The computer company is offering a 36-month loan at a quoted interest rate of 5.9% with no money down. What will your monthly payments be? What is the effective annual rate on this loan?

**5. **BUS 342 - Muge Tiryakioglu 4. Calculating Number of Periods One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $300 per month. You will charge 1.5 percent per month interest on the overdue balance. If the current balance is $11,814.08, how long will it take for the account to be paid off?

**6. **BUS 342 - Muge Tiryakioglu 5. Calculating Annuity Values You want to have $25,000 in your savings account five years from now, and you are prepared to make equal annual deposits into the account at the end of each year. If the account pays 9.5 percent interest, what amount must you deposit each year?

**7. **BUS 342 - Muge Tiryakioglu 6. Calculating Annuity Values You are interested in saving money for your first house. Your plan is to make regular deposits into a brokerage account which will earn 14%. Your first deposit of $5,000 will be made today. You also plan to make four additional deposits at the beginning of each of the next four years. You plan is to increase deposits by 10% a year (e.g., your second deposit $5,500, etc.). How much money will be in your account after five years?

**8. **BUS 342 - Muge Tiryakioglu 7. Calculating Annuity Values You believe that you will spend $40,000 a year for 20 years once you retire in 40 years. If the interest rate is 4 percent per year, how much must you save each year until retirement to meet your goal?
How much would you need to save if you believe that you will inherit $100,000 in 10 years?

**9. **BUS 342 - Muge Tiryakioglu 8. Present Value with Multiple Cash Flows In January 1984, Richard “Goose” Gossage signed a contract to play for the San Diego Padres that guaranteed him a minimum of $9,950,000. The guaranteed payments were $875,000 for 1984, $650,000 for 1985, $800,000 for 1986, $1 million for 1987, $1 million for 1988, and $300,000 for 1989. In addition, the contract called for $5,330,000 in deferred money payable at the rate of $240,000 per year from 1990 through 2006 and then $125,000 a year from 2007 through 2016. If the interest rate was 9 percent and the payments were to be made on July 1 of each year, what would be the present value of these payments on January 1, 1984?

**10. **BUS 342 - Muge Tiryakioglu Present Value with Multiple Cash Flows If Gossage were to receive an equal salary at the end of each of the five years from 1984 to 1988, what would his equivalent annual salary be?

**11. **BUS 342 - Muge Tiryakioglu 9. Perpetual Cash Flows What is the value of an investment that pays $7,500 every other year forever, if the first payment occurs one year from today and the discount rate is 15 percent per year compounded monthly? What is the value today if the first payment occurs four years from today?

**12. **BUS 342 - Muge Tiryakioglu 10. Calculating Annuities Due A ten-year annual annuity due with the first payment occurring at date N=5 has a current value of $25,000. If the discount rate is 16 percent per year, what is the annuity payment amount?

**13. **BUS 342 - Muge Tiryakioglu 11. Deferred Annuities A 7-year annuity of 14 $8,000 payments will begin 6 years from now, with the first payment coming 6.5 years from now. If the discount rate is 18 percent compounded monthly, what is the value of this annuity 4 years from now?

**14. **BUS 342 - Muge Tiryakioglu 12. Deferred Perpetuity Given an interest rate of 14 percent compounded semiannually, what is the value a t=5 of a perpetual stream of $5,000 payments made annually that begin at date t=12?