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# 1 Foundation EQ answer file - 1[Future Value Five friends...

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HADM2222, Prof. Q. Ma, Fall 2009 1 1. [Future Value] Five friends all open investment accounts today. Which one will withdraw the largest amount of money from their account assuming that they each withdraw their funds at the end of their initial investment period? Anthony invests \$1,000 for eight years at 6% simple interest. Bryan invests \$1,000 for four years at 9% with interest compounded annually. Crystal invests \$800 for ten years at 11% with interest compounded annually. Daniel invests \$1,200 for six years at 8% simple interest. Elizabeth invests \$900 for nine years at 9% with interest compounded annually. Solution: A: 1,000*(1+.06*8) = 1,480 B: 1,000*(1+.09) 4 = 1,411.58 C: 800*(1+.11) 10 = 2,271.54 D: 1,200*(1+6*.08) = 1,776 E: 900*(1+.09) 9 = 1,954.70 2. [FV as Growth Formula] The net sales for Wal-Mart of year 2007 were about \$350 billions. Suppose the net sales grow by 3% for the next 4 years. What will be the net sales for year 2011? Solution : FV formula used for growth. Here we have T=4, r=3% and PV=350. FV is 350*(1+.03) 4 = \$393.93. 3. [Present Value] To settle a lawsuit, Bill decided to pay Monica \$3,000 in ten years. If the discount rate for Monica is 10%, how much is the settlement worth to her? Solution : We have FV=3,000; r=10% and T=10; we need PV. PV= 3,000/(1+.10) 10 = 1,156.63. 4. [What’s Present?] Your parents set up a trust fund for you 10 years ago that is now worth \$19,671.51. If the fund earned 7% per year, how much did your parents invest? Solution : We have FV=19,671.51; r=7%; T=10; we need PV. PV = 19,671.51/(1+.07) 10 = 10,000

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HADM2222, Prof. Q. Ma, Fall 2009 2 5. [Discount Rate] You are looking at an investment that will pay \$1900 in 5 years if you invest \$1000 today. What is the implied rate of interest? Solution : FV = 1,900; PV=1,000; T=5; we need r. r= (1900/1000) 1/5 – 1 = 13.69%. 6. [Discount Rate] You have landed a fabulous investment opportunity, which can double your money in 10 years. How good is it? Solution : FV = 2; PV=1; T=10; we need r. r=(2/1) 1/10 – 1 = 7.18%. 7. [Implied Rate] Uncle Sam needs quick cash for an emergency and goes to his best friends Barack and John. Barack offers him \$20 million to pay back \$24 million in five years, while John offers him \$20 million to pay back \$25 million in six years. Which deal is better for Uncle Sam? Solution: Barack: FV=24, PV=20, T=5, we need r. r=(24/20) 1/5 – 1 = 3.71% John: FV=25, PV=20, T=6, we need r. r=(25/20) 1/6 – 1 = 3.79% It seems Barack is charging a lower rate of return. 8. [Invest for Next Generation] Suppose you have a 1-year old son and you want to provide \$750,000 in 17 years towards his college education. You currently have \$50,000 to invest. What interest rate must you earn to have the \$750,000 when you need it? Solution: PV=50,000; FV=750,000; T=17; we need r. r=(750,000/50,000) 1/17 – 1 = 17.27%. 9. [Number of Periods] You expect to receive \$250,000 in two years upon graduation. When you receive it, you will invest it at 7.9 percent per year and plan to withdraw till it reaches \$1 million. How long will it take? Solution : PV=250,000; FV=1,000,000; r=7.9%; we need T. T=ln(1,000,000/250,000)/ln(1+.079) = 18.23. It takes 18.23 years after receiving the \$250,000 at graduation.
HADM 2222 Fall 2009 Prof. Q. Ma 1 / 6 1. [FV] Suppose you invest \$500 in a mutual fund today and \$600 in one year. If the fund pays 9% annually, how much will you have in two years?

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1 Foundation EQ answer file - 1[Future Value Five friends...

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