m03_broo6637_1e_im_c03

Answers to End-of-Chapter Problems

1. Future Values. Fill in the future values for the following table,

a. using the future value formula, FV PV (1 r)n.b. using the time value of money keys or function from a calculator or spreadsheet.

Present Value Interest Rate Number of Periods Future Value

$ 400.00 5.0% 5

$17,411.00 6.0% 30

$35,000.00 10% 20

$26,981.75 16% 15

Answer:

Present Value Interest Rate Number of Periods Future Value

$ 400.00 5.0% 5 $ 510.51

$17,411.00 6.0% 30 $ 99,999.92

$35,000.00 10% 20 $235,462.50

$26,981.75 16% 15 $249,999.97

a. With the TVM Formula (rounding to second decimal only for final answer),

FV $400.00 (1.05)5 $400.00 1.2763 $510.51

FV $17,411.00 (1.06)30 $17,411.00 5.7435 $99,999.92

FV $35,000.00 (1.10)20 $35,000.00 6.7275 $235,462.50

FV $26,981.75 (1.16)15 $26,981.75 9.2655 $249,999.97

©2010 Pearson Education, Inc. Publishing as Prentice Hall

41 Brooks • Financial Management: Core Concepts

b. Time Value of Money Keys or Spreadsheet

Input 5 5.0 400 0

Variable N I/Y PV PMT FV

Compute 510.51

Input 30 6.0 17,411 0


Compute 99,999.92

Input 20 10.0 35,000 0


Compute 235,462.50

Input 15 16.0 26,981.75 0


Compute 249,999.97

2. Future Value (with changing years). Dixie Bank offers a certificate of deposit with an option to select your own investment period. Jonathan has $7,000 for his CD investment. If the bank is offering a 6% interest rate, how much will the CD be worth at maturity if Jonathan picks a

a. two-year investment period?b. five-year investment period?c. eight-year investment period?d. fifteen-year investment period?

Answer: a. FV $7,000 (1.06)2 $7,000 1.1236 $7,865.20

b. FV $7,000 (1.06)5 $7,000 1.3382 $9,367.58

c. FV $7,000 (1.06)8 $7,000 1.5938 $11,156.94

d. FV $7,000 (1.06)15 $7,000 2.3966 $16,775.91

3. Future Value (with changing interest rates). Jose has $4,000 to invest for a two-year period. He is looking at four different investment choices. What will be the value of his investment at the end of two years for each of the following potential investments?

a. bank CD at 4%.b. bond fund at 8%.c. mutual stock fund at 12%.d. new venture stock at 24%.

Answer: a. FV $4,000 (1.04)2 $4,000 1.0816 $4,326.40

b. FV $4,000 (1.08)2 $4,000 1.1664 $4,665.60

c. FV $4,000 (1.12)2 $4,000 1.2544 $5,017.60

d. FV $4,000 (1.24)2 $4,000 1.5376 $6,150.40


Chapter 3 The Time Value of Money (Part 1) 42

4. Future Value. Grand Opening Bank is offering a one-time investment opportunity for its new customers. A customer opening a new checking account can buy a special savings bond for $100 today, which the bank will compound at 7.5% for the next twenty years. The savings bond must be held for at least five years but can then be cashed in at the end of any year starting with year five. What is the value of the bond at each cash-in date up through twenty years? (Use an Excel spreadsheet to solve this problem.)

Spreadsheet Solution:

In Cells A1 through A16 put in the Present Value of the savings bond, $100.00.

In Cells B1 through B16 put in the annual interest rate, 0.075, R.

In Cells C1 through C16 put in the waiting time in years, 5 through 20, N.

In Cell D1 put in the FV function using the row value in A1 for the PV, row value in B1 for the interest rate, row value in C1 for n. Copy the formula for cells D2 through D16.

The displayed value will be the future value of the $100 savings bond at 7.5% annual interest.

A B C D

1 100.00 0.075 5 FV (PV A1, rate B1, n C1) $143.56

2 100.00 0.075 6 FV (PV A2, rate B2, n C2) $154.33

3 100.00 0.075 7 FV (PV A3, rate B3, n C3) $165.90

4 100.00 0.075 8 FV (PV A4, rate B4, n C4) $178.35

5 100.00 0.075 9 FV (PV A5, rate B5, n C5) $191.72

6 100.00 0.075 10 FV (PV A6, rate B6, n C6) $206.10

7 100.00 0.075 11 FV (PV A7, rate B7, n C7) $221.56

8 100.00 0.075 12 FV (PV A8, rate B8, n C8) $238.18

9 100.00 0.075 13 FV (PV A9, rate B9, n C9) $256.04

10 100.00 0.075 14 FV (PV A10, rate B10, n C10) $275.24

11 100.00 0.075 15 FV (PV A11, rate B11, n C11) $295.89

12 100.00 0.075 16 FV (PV A12, rate B12, n C12) $318.08

13 100.00 0.075 17 FV (PV A13, rate B13, n C13) $341.94

14 100.00 0.075 18 FV (PV A14, rate B14, n C14) $367.58

15 100.00 0.075 19 FV (PV A15, rate B15, n C15) $395.15

16 100.00 0.075 20 FV (PV A16, rate B16, n C16) $424.79

Note: The negative values in column A denote the cash outflow and produce a positive cash inflow in column D.

5. Future Value. Jackson Enterprises has just purchased some land for $230,000. The land was purchased for a future beach front property development project that will include rental



cabins, lodge, and recreational facilities. Jackson Enterprises has not committed to the development project, but will decide in five years whether to go forward with it or sell off the land. Real estate values increase annually at 4.5% for unimproved property in this area. For how much can Jackson Enterprises expect to sell the property in five years if it chooses not to proceed with the beach front development project? What if Jackson Enterprises holds the property for ten years and then sells?

Answer: Holding Property Five Years:

FV $230,000 (1.045)5 $230,000 1.2462 $286,621.85

Holding Property Ten Years:

FV $230,000 (1.045)10 $230,000 1.5530 $357,182.97

6. Future Value. The Portland Stallions professional football team is looking at its future revenue stream from ticket sales. Currently, a season package costs $325 per seat. The season ticket holders have been promised this same rate for the next three years. Four years from now, the organization will raise season ticket prices based on the estimated inflation rate of 3.25%. What will the season tickets sell for in four years?

Answer: FV $325 (1.0325)4 $325 1.136475928 $369.35

7. Future Value. Upstate University charges $16,000 a year in graduate tuition. Tuition rates are growing at 4.5% each year. You plan on enrolling in graduate school in five years. What is your expected graduate tuition in five years?

Answer: FV $16,000 (1.045)5 $16,000 1.246181938 $19,938.91

8. Present Values. Fill in the present values for the following table,

a. using the present value formula, PV FV (1/(1 r )n).b. using the TVM keys or function from a calculator or spreadsheet.

Future Value Interest Rate Number of Periods Present Value

$ 900.00 5% 5 ?

$ 80,000.00 6% 30 ?

$350,000.00 10% 20 ?

$ 26,981.75 16% 15 ?

Answer:

Future Value Interest Rate Number of Periods Present Value

$ 900.00 5% 5 $ 705.17

$ 80,000.00 6.0% 30 $13,928.81

$350,000.00 10% 20 $52,025.27

$ 26,981.75 16% 15 $ 2,912.06

a. With TVM Formula (rounding to second decimal only for final answer),



PV $900.00 1/(1.05)5 $400.00 0.7835 $705.17PV $80,000.00 1/(1.06)30 $80,000.00 0.1741 $13,928.81

PV $350,000.00 1/(1.10)20 $350,000.00 0.1486 $52,025.27

PV $26,981.75 1/(1.16)15 $26,981.75 0.1079 $2,912.06




Input 5 5.0 0 900


Compute 705.17

Input 30 6.0 0 80,000


Compute 13,928.81

Input 20 10.0 0 350,000


Compute 52,025.27

Input 15 6.0 0 26,981.75


Compute 2,912.06

9. Present Value (with changing years). When they are first born, Grandma gives every grandchild a $2,500 savings bond that matures in eighteen years. For each of the following grandchildren, what is the present value of each savings bonds if the current discount rate is 4%?

a. Seth turned sixteen years old today.b. Shawn turned thirteen years old today.c. Sherry turned nine years old today.d. Sheila turned four years old today.e. Shane was just born.

Answer: a. PV $2,500 1/(1.04)2 $2,500 0.9246 $2,311.39

b. PV $2,500 1/(1.04)5 $2,500 0.8219 $2,054.82

c. PV $2,500 1/(1.04)9 $2,500 0.7026 $1,756.47

d. PV $2,500 1/(1.04)14 $2,500 0.5775 $1,443.69

e. PV $2,500 1/(1.04)18 $2,500 0.4936 $1,234.07

10. Present Value (with changing interest rates). Marty has been offered an injury settlement of $10,000 payable in three years. He wants to know what the present value of the injury settlement is if his opportunity cost is 5%. (The opportunity cost is the interest rate in this problem.) What if the opportunity cost is 8%? What if it is 12%?

Answer: PV $10,000 1/(1.05)3 $10,000 0.8638 $8,638.38

PV $10,000 1/(1.08)3 $10,000 0.7938 $7,938.32

PV $10,000 1/(1.12)3 $10,000 0.7118 $7,117.80



11. Present Value. The State of Confusion wants to change the current retirement policy for state employees. To do so, however, the state must pay the current pension fund members the present value of their promised future payments. There are 240,000 current employees in the state pension fund. The average employee is twenty-two years away from retirement, and the average promised future retirement benefit is $400,000 per employee. If the state has a discount rate of 5% on all its funds, how much money will the state have to pay to the employees before it can start a new pension plan?

Answer: Present Value of Retirement Payments of the Average Employee:

PV $400,000 1/(1.05)22 $400,000 0.3418 $136,739.95

With 240,000 employees, the Total Obligations Are:

PV Obligation of Pension Fund 240,000 $136,739.95 $32,817,590,000

Note, the PV was not rounded to nearest cent prior to multiplying it by the number of employees.

12. Present Value. Two rival football fans have made the following wager: if one fan’s college football team wins the conference title outright, the other fan will donate $1,000 to the winning school. Both schools have had relatively unsuccessful teams but are improving each season. If the two fans must put up their potential donation today and the discount rate is 8% for the funds, what is the required upfront deposit if a team is expected to win the conference title in five years? Ten years? Twenty years?

Answer: Present Value of Payoff in Five Years:

PV $1,000 1/(1.08)5 $1,000 0.6806 $680.58

Present Value of Payoff in Ten Years:

PV $1,000 1/(1.08)10 $1,000 0.4632 $463.19

Present Value of Payoff in Twenty Years:

PV $1,000 1/(1.08)20 $1,000 0.2145 $214.55

13. Present Value. Prestigious University is offering a new admission and tuition payment plan for all alumni. On the birth of a child, parents can guarantee admission to Prestigious if they pay the first year’s tuition. The university will pay an annual rate of return of 4.5% on the deposited tuition, and a full refund will be available if the child chooses another university. The tuition is $12,000 a year at Prestigious and is frozen at that level for the next eighteen years. What would parents pay today if they just gave birth to a new baby and the child will attend college in eighteen years? How much is the required payment to secure admission for their child if the interest rate falls to 2.5%?

Answer: PV $12,000 1/(1.045)18 $12,000 1/(2.2085) $12,000 0.4528 $5,433.60

PV $12,000 1/(1.025)18 $12,000 1/(1.5597) $12,000 0.6412 $7,693.99



14. Present Value. Standard Insurance is developing a long-life insurance policy for people who outlive their retirement nest egg. The policy will pay out $250,000 on your eighty-fifth birthday. You must buy the policy on your sixty-fifth birthday. The insurance company can earn 7% on the purchase price of your policy. What is the minimum purchase price the insurance company should charge for this policy?

Answer: PV $250,000 1/(1 0.07)20 $250,000 0.258419 $64,604.75

15. Present Value. You are currently in the job market. Your dream is to earn a six-figure salary ($100,000). You hope to accomplish this goal within the next thirty years. In your field, salaries grow at 3.75% per year. What starting salary do you need to reach this goal?

Answer: PV $100,000 1/(1 0.0375)30 $100,000 0.3314033 $33,140.33

16. Interest Rate or Discount Rate. Fill in the interest rate for the following table

a. using the interest rate formula, r (FV/PV)1/ n 1.b. using the TVM keys or function from a calculator or spreadsheet.

Present Value Future Value Number of Periods Interest Rate

$ 500.00 $ 1,998.00 18 ?

$17,335.36 $230,000.00 30 ?

$35,000.00 $ 63,214.00 20 ?

$27,651.26 $225,000.00 15 ?

Answer:

Present Value Future Value Number of Periods Interest Rate

$ 500.00 $ 1,998.00 18 8.00%

$17,335.36 $230,000.00 30 9.00%

$35,000.00 $ 63,214.00 20 3.00%

$27,651.26 $225,000.00 15 15.00%

a. With the TVM Formula (rounding to second decimal only for final answer)

r ($1998.00/$500.00)1/18 1 1.0800 1 8.00%r ($230,000/$17,335.36)1/30 1 1.0900 1 9.00%r ($63,214/$35,000)1/20 1 1.0300 1 3.00%r ($225,000/$27,651.26)1/15 1 1.1500 1 15.00%




Input 18 500.00 0 1,998.00


Compute 8.00

Input 30 17,335.36 0 230,000


Compute 9.00

Input 20 35,000 0 63,214


Compute 3.00

Input 15 27,651.26 0 225,000


Compute 15.00

17. Interest rate (with changing years). Keiko is looking at the following investment choices and wants to know what interest rate each choice produces.

a. Invest $400 and receive $786.86 in ten years.b. Invest $3,000 and receive $10,927.45 in fifteen years.c. Invest $31,180.47 and receive $100,000 in twenty years.d. Invest $31,327.88 and receive $1,000,000 in forty-five years.

Answer: a. r ($786.86/$400)1/10 1 1.07 1 7.00%

b. r ($10,927.45/$3,000)1/15 1 1.09 1 9.00%

c. r ($100,000/$31,180.47)1/20 1 1.06 1 6.00%

d. r ($1,000,000/$31,327.88)1/45 1 1.08 1 8.00%

18. Interest Rate. Two mutual fund managers, Martha and David, have been bragging that their fund is the top performer. Martha states that investors bought shares in the mutual fund ten years ago for $21.00 and those shares are now worth $65.00. David states that investors bought shares in his mutual fund for only $3.00 six years ago and now they are worth $7.30. Which mutual fund manager has had the highest growth rate for the management periods? Should this comparison be made over different management periods? Why or why not?

Answer: Martha’s Rate, r ($65.00/$21.00)1/10 1 1.1196 1 11.96%

David’s Rate, r ($7.30/$3.00)1/6 1 1.1598 1 15.98%

Fund Two has the higher annual return but for a shorter period of time. To be appropriate for comparing performance, the funds should be evaluated over the same period of time. The first fund may have had a higher return over the last six years than the second fund, but low returns in the earlier years reduced the return below the 16% return rate of the second fund.



19. Interest Rate. In 1972, Bob purchased a new Datsun 240Z for $3,000. Datsun later changed its name to Nissan, and the 1972 240Z became a classic. Bob kept his car in excellent condition and in 2002 could sell the car for six times what he originally paid. What was Bob’s return on owning this car? What if he keeps the car for another thirty years and earns the same rate? What could he sell the car for in 2032?

Answer: Thirty years’ return on car:

r ($18,000/$3,000)1/30 1 1.0615 1 6.15%

Price thirty years from now:

FV $18,000 (1.0615)30 $108,000

Or just increase the price six-fold again, $18,000 6 $108,000.

20. Interest Rate. Upstate Bank is offering long-term certificates of deposit with a face value of $100,000 (future value). Bank customers can buy these CDs today for $67,000 and will receive the $100,000 in fifteen years. What interest rate is the bank paying on these CDs?

Answer: r ($100,000/$67,000)1/15 1 1.027058 1 2.7058%

21. Discount rate. Future Bookstore sells books before they are published. Today, they are offering the book Adventures in Finance for $14.20, but the book will not be published for another two years. The retail price when the book is published will be $24. What is the discount rate Future Bookstore is offering its customers for this book?

Answer: r ($24/$14.20)1/2 1 1.30 1 30%

22. Growth and Future Value. A famous disease control scientist is trying to determine the potential infected population of the new West Columbia flu. Two weeks ago, the first patient showed up with the disease. Four days later the disease control center in Atlanta had six confirmed cases. The scientist estimates that it will be another two days before a cure will be ready, a total of 16 days from the first confirmed case. How many patients will be infected two days from now?

Answer: The disease is spreading at a growth rate of nearly 57% per day.

r (6/1)1/4 1 1.3161 1 56.51%

Using the same growth rate for the 16-day period, (two weeks and two days), we determine that the number of patients infected will be:

FV 1 (1.5156)16 1,296 or 1,296 patients

Or you could realize that every four days the number of people infected increases by six times, and with four periods of four days you have

1 6 6 6 6 1 (6)4 1,296.



23. Waiting Period. Fill in the number of periods for the following table.

a. using the waiting period formula, n ln(FV/PV)/ln(1 r).b. using the TVM keys or function from a calculator or spreadsheet.

Present Value Future Value Interest Rate Number of Periods

$ 800.00 $ 1,609.76 6% ?

$17,843.09 $ 100,000.00 9% ?

$35,000.00 $3,256,783.97 12% ?

$25,410.99 $ 300,000.00 28% ?

Answer: Solutions with Formula, TVM Keys, and Spreadsheet

Present Value Future Value Interest Rate Number of Periods

$ 800.00 $ 1,609.76 6% 12

$17,843.09 $ 100,000.00 9% 20

$35,000.00 $3,256,783.97 12% 40

$25,410.99 $ 300,000.00 28% 10

a. With the TVM Formula (rounding to second decimal only for final answer)

n ln($1,609.76/$800.00)/ln(1.06) 0.6992/0.0583 12n ln($100,000/$17,843.09)/ln(1.09) 1.7236/0.0862 20n ln($3,256,783.97/$35,000)/ln(1.12) 4.5331/0.1133 40n ln($300,000/$25,410.99)/ln(1.28) 2.4686/0.2469 10

b. Time Value of Money Keys or Spreadsheet Inputs

Input 6.00 800.00 0 1,609.76


Compute 12

Input 9.00 17,843.09 0 100,000


Compute 20

Input 12.0 35,000 0 3,256,783.97


Compute 40

Input 28.0 25,410.99 0 300,000


Compute 10



24. Waiting period (with changing years). Jamal is waiting to be a millionaire. He wants to know how long he must wait if

a. he invests $24,465.28 at 16% today?b. he invests $47,101.95 at 13% today?c. he invests $115,967.84 at 9% today?d. he invests $295,302.77 at 5% today?

Answer: a. n ln($1,000,000/$24,465.28)/ln(1.16) 3.7105/0.1484 25

b. n ln($1,000,000/$47,101.95)/ln(1.13) 3.0554/0.1222 25

c. n ln($1,000,000/$115,967.84)/ln(1.09) 2.1544/0.0862 25

d. n ln($1,000,000/$295,302.77)/ln(1.05) 1.2198/0.0488 25

25. Waiting Period. Jeff, a local traffic engineer, has designed a new pedestrian footbridge. The bridge has been designed to handle 200 pedestrians daily. Once the bridge reaches 1,000 pedestrians daily, however, it will require a new bracing system. Jeff has estimated that traffic will increase annually at 5%. How long will the current bridge system work before a new bracing system is required? What if the annual traffic rate increases at 8% annually? At what traffic increase rate will the current system last only ten years?

Answer: For 5% growth rate in pedestrian traffic:

n ln(1000/200)/ln(1.05) 1.6904/0.0488 32.9869 years

For 8% growth rate in pedestrian traffic:

n ln(1000/200)/ln(1.08) 1.6904/0.0770 20.9124 years

Ten years maximum would require a growth rate of:

r (1000/200)1/10 1 1.1746 1 17.46%

26. Waiting Period. Susan Norman seeks your financial advice. She wants to know how long it will take for her to become a millionaire. She tells you that she has $1,330 today and wants to invest it in an aggressive stock portfolio. The historical return on this type of investment is 18% per year. How long will she have to wait if the $1,330 is the only amount she invests and she never withdraws from the market until she reaches her million dollars? (Assume no taxes on the earnings). What if the rate of return is only 14% annually? What if the rate of return is only 10% annually?

Answer: Waiting time if investment is earning 18%:

n ln(1,000,000/1,330)/ln(1.18) 6.6226/0.1655 40.0121 years

Waiting time if investment is earning 14%:

n ln(1,000,000/1,330)/ln(1.14) 6.6226/0.1310 50.5431 years

Waiting time if investment is earning 10%:

n ln(1,000,000/1,330)/ln(1.10) 6.6226/0.0953 69.4845 years



27. Waiting Period. Upstate University currently has a 6,000-car parking capacity for faculty, staff, and students. This year, the university issued 4,356 parking passes. Parking passes have been growing at a rate of 6% per year. How long will it be before the university will need to add additional parking?

Answer: Waiting time if parking growth rate is 6%:

n ln(6,000/4,356)/ln(1.06) 0.320305264/0.058268908 5.4953 years

28. Double Your Money. Approximately how long will it take to double your money if you get 5.5%, 7.5%, or 9.5% annual return on your investment? Verify the approximate doubling period with the time value of money equation.

Answer: Approximating the double period with the Rule of 72s:

At 5.5%, 72/5.5 13.09, or a little over 13 yearsAt 7.5%, 72/7.5 9.60, or a little over 9 1/2 yearsAt 9.5%, 72/9.5 7.5789, or a little over 7 1/2 years

Verification:

n ln 2/ln 1.055 0.6931/0.0535 12.9462, or a little under 13 yearsn ln 2/ln 1.075 0.6931/0.0723 9.5844, or a little over 9 1/2 years n ln 2/ln 1.095 0.6931/0.0908 7.6376, or a little over 7 1/2 years

29. Double Your Wealth. Kant Miss Company is promising its investors that it will double their money every three years. Is this promise too good to be true? What annual rate is Kant Miss promising? If you invested $250 now and Kant Miss was able to deliver on its promise, how long would it take before your investment reaches $32,000?

Answer: According to the rule of 72s, the approximate rate is: 72/3 24%

The actual rate is: r 21/3 1 25.99%

To calculate how long it would take for $250 to turn into $32,000:

n ln(32,000/250)/ln(1.2599) 21 years

30. Challenge Question. In the text chapter, we dealt exclusively with a single lump sum, but often we may be looking at several lump-sum values simultaneously. Let’s consider the retirement plan of a couple. Currently, the couple has four different investments: a 401(k) plan, two pension plans, and a personal portfolio. The couple is five years away from retirement. They believe they have sufficient money in their plans today so that they do not have to contribute to the plans over the next five years and will still meet their $2 million retirement goal. Here are the current values and the growth rate of each plan:

401(k): $88,000 growing at 6.5%Pension Plan 1: $304,000 growing at 7%Pension Plan 2: $214,000 growing at 7.25%Personal Portfolio: $149,000 growing at 8.5%

Does the couple have enough already invested to make their goal in five years?

Hint: View each payment as a separate problem and find the future value of each lump sum. Then add up all the future values five years from now.



Answer: Future Value of 401(k) $88,000 (1.065)5 $88,000 1.3701 $120,567.63

Future Value of Pension Plan 1: $304,000 (1.07)5 $304,000 1.4026 $426,375.73

Future Value of Pension Plan 2: $214,000 (1.0725)5 $214,000 1.4190 $303,668.87

Future Value of Personal Portfolio: $149,000 (1.085)5 $149,000 1.50365 $224,043.85

Total $120,567.63 $426,375.73 $303,668.87 $224,043.85 $1,074,656.08

They are only half way to their $2 million dollar goal with their current savings, pensions, and 401(k) plan.

Additional Problems with Answers

1. Joanna’s Dad is looking to deposit a sum of money immediately into an account that pays an annual interest rate of 9% so that her first-year college tuition costs are provided for. Currently, the average college tuition cost is $15,000 and is expected to increase by 4% (the average annual inflation rate). Joanna just turned 5, and is expected to start college when she turns 18. How much money will Joanna’s Dad have to deposit into the account? (Slides 3-36–3-38)

Answer: Step 1. Calculate the average annual college tuition cost when Joanna turns 18, i.e., the future compounded value of the current tuition cost at an annual increase of 4%.

PV 15,000; n 13; i 4%; PMT 0; CPT FV $24, 976.10 (rounded to 2 decimals)

OR

FV $15,000 (1.04)13 $15,000 1.66507 $24,976.10

Step 2. Calculate the present value of the annual tuition cost using an interest rate of 9% per year.

FV 24,976.10; n 13; i 9%; PMT 0; CPT PV $8,146.67 (rounded to 2 decimals)

OR

PV $24,976.10 (1/(1 0.09)13 $24,976.10 0.32618 $8,146.67

So, Joanna’s Dad will have to deposit $8,146.67 into the account today so that she will have her first-year tuition costs provided for when she starts college at the age of eighteen.



2. Bank A offers to pay you a lump sum of $20,000 after five years if you deposit $9,500 with them today. Bank B, on the other hand, says that they will pay you a lump sum of $22,000 after five years if you deposit $10,700 with them today. Which offer should you accept and why? (Slides 3-39–3-41)

Answer: To answer this question, you have to calculate the rate of return that will be earned on each investment and accept the one that has the higher rate of return.

Bank A’s Offer:

PV $9,500; n 5; FV $20,000; PMT 0; CPT I 16.054%

OR

Rate (FV/PV)1/n 1 ($20,000/$9,500)1/5 1 1.16054 1 16.054%

Bank B’s Offer:

PV $10,700; n 5; FV $22,000; PMT 0; CPT I 15.507%

OR

Rate (FV/PV)1/n 1 ($22,000/$10,700)1/5 1 1.15507 1 15.507%

You should accept Bank A’s offer, since it provides a higher annual rate of return.

3. You have decided that you will sell off your house, which is currently valued at $300,000, at a point when it appreciates in value to $450,000. If houses are appreciating at an average annual rate of 4.5% in your neighborhood, for approximately how long will you be staying in the house? (Slides 3-42–3-43)

Answer: PV 300,000; FV 450,000; i 4.5%; PMT 0; CPT n 9.21 years or 9 years and 3 months

OR

n [ln(FV/PV)]/[ln(1 i)]n [ln(450,000/(300,000])/[ln(1.045)] .40547/.04402 9.21 years

4. Your arch-nemesis, who happens to be an accounting major, makes the following remark, “You finance types think you know it all…well, let’s see if you can tell me, without using a financial calculator, what rate of return an investor would have to earn in order to double $100 in 6 years?” How would you respond? (Slides 3-44–3-46)

Answer: Use the rule of 72 to silence him once and for all, and then prove the answer by compounding a sum of money at that rate for 6 years to show him how close your response was to the actual rate of return…Then ask him politely if he would like you to be his “lifeline” on “Who Wants to be a Millionaire?”

Rate of return required to double a sum of money 72/N 72/6 12%

Verification: $100(1.12)6 $197.38…which is pretty close to double.



The accurate answer would be calculated as follows:

PV 100; FV 200; n 6; PMT 0; I 12.246%

OR

r (FV/PV)1/n 1 (200/100)1/ 6 1 1.12246 1 .12246 or 12.246%

5. You want to save $25,000 for a down payment on a house. Bank A offers to pay 9.35% per year if you deposit $11,000 with them, while Bank B offers 8.25% per year if you invest $10,000 with them. How long will you have to wait to have the down payment accumulated under each option? (Slides 3-47–3-48)

Answer: Bank A:

FV $25,000; I 9.35%; PMT 0; PV 11,000; CPT N 9.18 years

Bank B:

FV $25,000; I 8.25%; PMT 0; PV 10,000; CPT N 11.558 years


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