Chapter 3

Double your money-Rule of 72. Approximately how long will it take to double your money if you get an annual return of 4.2%​, 6.5%​, or 9.5% on your​ investment?

a. 17.14 years 72/4.2=17.14 b. 11.08 years 72/6.5=11.08 c. 7.58 years 72/9.5=7.58

Double your wealth. Kant Miss Company is promising its investors that it will double their money every 2 years. What annual rate is Kant Miss​ promising? Is this investment a good​ deal? If you invest ​$450 now and Kant Miss is able to deliver on its​ promise, how long will it take your investment to reach ​$32,000​?

a. 36% rule of 72= 72/2=36% b.41.42% n=2 i=41.42 pv=1 pmt=0 fv=2 c. Yes. This investment is a good deal if you are earning lower than 41.42 rate of return annually on your current investment expl. compared to the rate of return that you can earn on your current investment d. 12.30 years n=12.30 i=41.42 pv=450 pmt=0 fv=32000

Interest rate. Two mutual fund​ managers, Martha and​ David, have been discussing whose fund is the top performer. Martha states that investors bought shares in her mutual fund 10 years ago for ​$26.00​, and those shares are now worth $55.00. David states that investors bought shares in his mutual fund 6 years ago for only ​$​2.30, and they are now worth $7.70. a. Which mutual fund manager had the higher growth rate for the management​ period? Should this comparison be made over different management​ periods? Why or why​ not? b. Which of the following statements is true?

a. David has had the highest growth rate of 22.31% for the management period. martha n=10 i=7.78 pv=26.00 pmt=0 fv=55.00 David n=6i=22.31 pv=2.30 pmt=0 fv=7.70 b. A valid comparison can only be made over the same management period due to changing market conditions. expl. The growth rate of David​'s mutual fund is 22.31​% which is higher than the 7.78​% growth rate of Martha​'s mutual fund. While David had the higher growth rate for the management​ period, due to changing market​ conditions, a valid comparison should only be made over the same management period.

Future value​ (with changing interest​ rates). Jose has $7,000 to invest for a 5​-year period. He is looking at four different investment choices. What will be the value of his investment at the end of 5 years for each of the following potential​ investments? a. Bank CD at 5% b. Bond Fund at 8% c. Mutual stock fund at 15% d. New venture stock at 23%

a. fv= $8933.97 n=5 i=5% pv=7000 pmt=0 b. fv= $10285.30 n=5 i=8% pv=7000 pmt=0 c. fv= $14079.50 n=5 i=15% pv=7000 pmt=0 d. fv= $ 19707.14 n=5 i=23% pv=7000 pmt=0

Waiting period. Jamal is waiting to be a millionaire. He wants to know how long he must wait if a. he invests $24290.76 at 19% today? b. he invests $52754.01 at 16% today?

a. n= 21 years n=21 i=19% pv=24290.76 pmt=0 fv=1,000,000 b. n= 20 years n=20 i=16% pv=52754.01 pmt=0 fv=1,000,000

Present value​ (with changing​ years). When they are first​ born, Grandma gives each of her grandchildren a ​$ savings bond that matures in 18 years. For each of the following​ grandchildren, what is the present value of each savings bonds if the current discount rate is ​%? a. Seth turned 16 years old today. e. Shane was just born.

a. pv= $3144.58 n=2 i=5.5% pmt=0 fv=3500 e. pv= $1335.13 n=18 i=5.5 pmt=0 fv=3500

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 ​6% on the deposited​ tuition, and a full refund will be available if the child chooses another university. The tuition is expected to be ​$18000 a year at Prestigious 19 years from now. What would parents pay today if they just gave birth to a new baby and the child will attend college in 19 ​years? How much is the required payment to secure admission for their child if the interest rate falls to ​2.5%?

a. pv= $5949.23 n=19 i=6% pmt=0 fv=18000 b. pv= $11259.50 n=19 i=2.5 pmt=0 fv=18000

Present value​ (with changing interest​ rates). Marty has been offered an injury settlement of ​$11000 payable in 4 years. He wants to know what the present value of the injury settlement is if his opportunity cost is 4.5​%. ​ (The opportunity cost is the interest rate in this​ problem.) What if the opportunity cost is ​8%? What if it is ​11%?

a. pv= $9224.18 n=4 i=4.5 pmt=0 fv=11000 b. pv= $8085.33 n=4 i=8 pmt=0 fv=11000 c. pv= $7246.04 n=4 i=11 pmt=0 fv=11000

Future value. Upstate University charges ​$22,000 a year in graduate tuition. Tuition rates are growing at 3.75​% each year. You plan to enroll in graduate school in 4 years. What is your expected graduate tuition in 4 years?

fv= $25490.31 expl. n=4 i= 3.75 pv=22000 pmt=0

Future value. The Portland Stallions professional football team is looking at its future revenue stream from ticket sales. ​ Currently, a season package costs $450 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 2.5​%. What will the season tickets sell for in 4 years?

fv= $496.72 n=4 i=2.5 pv=450 pmt=0

Future value​ (with changing​ years). Dixie Bank offers a certificate of deposit with an option to select your own investment period. Jonathan has $6,000 for his CD investment. If the bank is offering a 5.5​% interest​ rate, compounded​ annually, how much will the CD be worth at maturity if Jonathan picks a two-year investment?

fv= $6678.15 n=2 i=5.5 pv=6000 pmt=0

Discount rate. Future Bookstore sells books before they are published. ​Today, they are offering the book Adventures in Finance for ​$14.28​, but the book will not be published for another 3 years. The retail price when the book is published will be ​$23. What is the discount rate Future Bookstore is offering its customers for this​ book?

i= 17.22 n=3 i=17.22 pv=14.28 pmt=0 fv=23

Interest rate. In​ 1972, Bob purchased a new Datsun 240Z for ​$3200. Datsun later changed its name to​ Nissan, and the 1972 Datsun 240Z became a classic. Bob kept his car in excellent condition and in 2002 could sell the car for 6 times what he originally paid. What was​ Bob's annualized rate of return for the 30 years he owned this​ car? If he keeps the car for another 30 years and earns the same​ rate, what could he sell the car for in​ 2032?

i= 6.15% n=30 i=6.15 pv=3200 pmt=0 fv=19200 b. $115053.86 n=30 i=6.15 pv=19200 pmt=0 fv=115053.86

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 $200000 current employees in the state pension fund. The average employee is 16 years away from​ retirement, and the average promised future retirement benefit is ​$400000 per employee. If the state has a discount rate of 4​% on all its​ funds, how much money will the state have to pay to the employees before it can start a new pension​ plan?

pv= $42,712,654,055 n=16 i=4 pmt=0 fv=20000*400000= 80,000,000,000

Present value. You are currently in the job market. Your dream is to earn a​ six-figure salary ​($150000​). You hope to accomplish this goal within the next 28 years. In your​ field, salaries grow at 3​% per year. What starting salary do you need to reach this​ goal?

pv= $65,561.51 n=28 i=3 pmt=0 fv=150000