HW4

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Washington State University *

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102

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Finance

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Apr 3, 2024

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docx

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Chapter 5 - Exercises 1. Suppose you invest $500 today. If your investment pays 6% interest per year, how much will you have at the end of four years? Used Calculator: FV = 500 * (1+0.06)^4 = 631.24 2. Suppose you invest $5,000 in a bank CD that pays 1.2% interest per year. How much money will you receive when you cash in the CD in 5 years? Used Calculator: FV = 5,000 * (1+ 0.012)^5 = 5,307.29 3. Suppose you invest $5,000 in a bank CD that pays 1.2% interest per year, but it is compounded monthly. How much money will you receive when you cash in the CD in 5 years? [Hint: FV= PV ∗( 1 + r n ) nt ] *In this case, n=12 represents the number of times interest is compounded per year. Used Calculator: FV = 5,000 * (1 + 0.012/12)^(12*5) = 5,309.02 4. Suppose you receive a $10,000 gift from your rich aunt. You decide to invest the gift in the stock market by buying an S&P 500 ETF. Suppose the ETF earns 20% in the first year, 14% in the second year, -12% in the third year, 4% in the fourth year, and then 6% for three straight years. How much will your investment be worth after 7 years? Year 1 = 10,000 * (1 + .20) = 12,000 Year 2 = 12,000 * (1+.14) = 13,680 Year 3 = 13,680 * (1 + (-.12) = 13,680 * 0.82 = 11.217.60 Year 4 = 11,217.60 * (1 + 0.04) = 11,666.30 FV Year 5 - 7 = 11,666.30 * (1 + 0.06)^3 = 13,894.749 = 13,894.75
5. Suppose you buy 100 shares of Facebook (FB) Stock for $190 per share. At the end of 3 years, FB is selling for $310 per share. What return did you earn? State your answer as an APR (Annual percentage return). Used Calculator: PV = 19,000, FV = 31,000 Rate = 17.73% 31,000 = 19,000 (1+r)^3 Solve for r: 6. From question #4, what rate of return, stated in annual terms, did you earn on your investment? What was the average rate of return? [Hint: Avg rate= (r1+r2+…+r7)/7. For example, r1=20%, r2=14% ...... ] Avg rate = (20% + 14% + (-12%) + 4% + 6% + 6% + 6%) / 7 = 6.285 = 6.29% 7. Suppose you are confident you can earn 8% per year by investing in the stock market. If your goal is to be a millionaire in 15 years, how much would you need to invest today? Used Calculator: PV = 1,000,000 / (1+0.08)^15 PV = 315,241.70 8. How much would you be willing to pay for an investment that promises to pay you $100,000 in 20 years? Assume your required return on such an investment is 10% per year. Used Calculator: PV = 100,000 / (1+0.10)^20 = 100,000 / (1.10)^20 = 100,000/6.72749994933 PV = 14,864.3628 = 14,864.36 9. Suppose you paid $100,000 for an investment that promises to pay you $150,000 in 10 years. If you required return is 4% per year, was this a good deal? Used Calculator FV = 100,000 * (1.04)^10 = 148,024.43 No this is not a good deal since in 10 years with that return rate of 4% you would not be able to make the full $150,000 that was promised you would need to have a higher return rate. 10. If you invest $10,000 today in an account earning 8% per year, how many years until you have doubled your money? Tripled your money? Used Calculator: 20,000 = 10,000 * (1.08)^t T= 9.01 years 30,000 = 10,000 * (1.08)^t T = 14.27 years
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