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Solve the following application problems. 11.1 Exe 15. RETIREMENT PLANNING Darnell Johnson wants to know if he can retire in 35 years at age 60, when he plans to do a lot of fishing. Assume the deposit into his retirement account averages $3800 at the end of each year and that the funds earn 6% per year. Find (a) the amount of the annuity and (b) the interest earned. (a) $423, 452.16 (a) Amount = $3800 X 111.43478 = $423, 452.16 (b) $290, 452.16 (b) Interest = $423, 452.16 - 35 X $3800 = $290, 452.16 16. SAVING FOR A HOME Jim and Betty Collins need an additional $6500 for a down pay- ment on a home they hope to buy in 2 years. They invest $800 at the end of each quarter in (a) an account earning 6% compounded quarterly. Find (a) the amount of the annuity and (b) the interest earned. (b) 17. CHILDCARE PAYMENTS Monique Chaney places $250 of her quarterly child support check into an annuity for the education of her child. She does this at the beginning of each (a) quarter for 8 years into an account paying 8% per year, compounded quarterly. Find (a) the (b) amount of the annuity and (b) the interest earned. 18. RETIREMENT Jason Horton works for Chevron as a (a) welder on offshore drilling rigs. His retirement plan con- tributions are $3800 at the beginning of each 6-month ( b ) period. Assume that the account grows at 6% com- pounded semiannually for 15 years. Find the (a) future value of the annuity and (b) the interest earned. 19. MUTUAL FUND INVESTING Sandra Gonzales deposits $1000 into a mutual fund contain- 19. ing international stocks at the end of each semiannual period for 12 years. Assume the fund earns 10% interest compounded semiannually and find the future value. 20. T-BILL AND STOCK INVESTING Joann Gretz (see Example 4, page 413) decides to place 20. half of her $2000 deposit at the end of each year into the bond fund and half into the stock fund. Assume the bond fund earns 6% compounded annually and the stock fund earns 10% compounded annually. Find the amount available in 33 years. Page 415 Question 20422 CHAPTER 11 Annuities, Stocks, and Bonds 11.2 Exercises // MyLab Math The shaded sections below contain solutions to help you get a QUICK START on the various types of exercises. Find the present value of the following annuities. Round to the nearest cent. (See Examples 1-3.) Amount per Payment Payment at Time Rate of Present Compounded Value End of Each (Years) Investment 1. $1800 year 18 10% annually $14,762.54 Present value = $1800 X 8.20141 = $14,762.54 2. $4100 $22,887.76 year 5% annually Present value = $4100 X 5.58238 = $22,887.76 3. $2000 6 months 12 8% semiannually 4. $1700 6 months 14 5% semiannually 5. $894 quarter 6 4% quarterly 6. $7500 quarter 5 10% quarterly 7. Explain the two different ways to think of the present value of an annuity. (See Objective 1.) 8. Explain the meaning of equivalent cash price. (See Objective 3.) Page 422 Solve the following application problems. Question 4 9. INJURY LAWSUIT The court ruled that Locan Corporation was liable in the death of an employee. The settlement called for the company to pay the employee's widow $65,000 at 9. $810, 043.65 the end of each year for 20 years. Find the amount the company must set aside today, assuming 5% compounded annually. Present value of annuity = $65,000 X 12.46221 = $810, 043.65 C// 10. COMPUTER REPLACEMENT The hospital unit on which Darnell Johnson works sets aside an annual payment of $35,000 per year for 5 years so it will have funds to replace 10. the personal computers, servers, and printers when needed. Assuming 5% compounded annually, what lump sum deposited today would result in the same future value? 11. COLLEGE EXPENSES In addition to his scholarship, Benjamin Wink needs $8000 every 6 months for living expenses and tuition at his university. It will take 5 years to complete (a) his engineering degree. Assume funds earn 5% per year and find (a) the lump sum that (b) must be deposited to meet this need and (b) the interest earned.waits a OS - 30 - In the works on discussion 13. PAYING FOR COLLEGE Gabriel Martinez estimates that his daughter's college needs, 11.2 Exercises beginning in 8 years, will be $3600 at the end of each quarter for 4 years. (a) Find the total amount needed in 8 years assuming 8% compounded quarterly. (b) Will he have enough (a) money available in 8 years if he invests $700 at the end of each quarter for the next 8 years at 8% compounded quarterly? ( b ) 14. VAN PURCHASE In 4 years, Jennifer Videtto will need to purchase a delivery van for her plumbing company. She estimates it will require a down payment of $10,000 with pay- ments of $950 per month for 36 months. (a) Find the total amount needed in 4 years (a) (b ) assuming 12% compounded monthly. (b) Will she have enough if she invests $2200 at the end of every quarter for 4 years and earns 6% compounded quarterly? 15. SELLING A RESTAURANT Anna Stanley has two offers for her pizza business. The first offer is a cash payment of $85,000, and the second is a down payment of $25,000 with (a) payments of $3500 at the end of each quarter for 5 years. (a) Identify the better offer (b ) assuming 8% compounded quarterly. (b) Find the difference in the present values. 16. GROCERY STORE Adolf Hegman has two offers for his Canadian grocery company. The first offer is a cash payment of $540,000, and the second is a down payment of $240,000 (a) with payments of $65,000 at the end of each semiannual period for 4 years. (a) Identify the (b) better offer assuming 10% compounded semiannually. (b) Find the difference in the pre- sent values. 17. SOCIAL SECURITY Jessica Thames expects to receive $18,400 per year based on her 17. deceased husband's contributions to Social Security. Assume that she receives payments for 14 years and a rate of 4% per year, and find the present value of this annuity. 18. SOCIAL SECURITY Warren and Bernice White's combined Social Security payments add 18. up to $35,400 per year. Assume payments for 20 years and a rate of 6% per year, and find the present value. Page 423 Question 14$17,989,548 X .05577 = $1,003,277.09 Payments of $1,003,277.09 at the end of each quarter for 4 years into a sinking fund earning 6% compounded quarterly will result in the funds needed to purchase the jet. 0800% 6903 QUICK CHECK 4 0608 DELs The $19,000 cost of a compressor is increasing by 5% per year. First find the amount 270 needed to buy the compressor in 3 years. Then find the necessary semiannual payment a sinking fund for the purchase if funds earn 10% compounded semiannually. 52 96ESO 9LOVO Quick TIP / Two different interest rates are involved in Example 4. The price is increasing at 5% 8LOVO Banks make money by charging more interest on money loaned year compounded annually, but deposits in the sinking fund earn 6% compounded quart 03575 out than they pay on funds Interest rate spreads such as these are common. For example, banks use the difference 03147 deposited at the bank. between interest rates on deposits and interest rates charged on loans to make money. .02782 .02466 .02193 11.3 Exercises / MyLab Math .01955 The shaded sections below contain solutions to help you get a QUICK START on the various types of exercises. .01746 01562 Find the amount of each payment needed to accumulate the indicated amount in a sinking fund. 01401 (See Examples 1-3.) 01257 1. $12,000, money earns 5% compounded annually, 4 years 1. $2784.12 1130 Payment = $12,000 X .23201 = $2784.12 017 2. $125,000, money earns 6% compounded annually, 25 years 2. $2278.75 25 Payment = $125,000 X .01823 = $2278.75 26 3. $8200, money earns 6% compounded semiannually, 5 years 3. 27 4. $12,000, money earns 10% compounded semiannually, 3 years 4 5. $50,000, money earns 4% compounded quarterly, 5 years 5. 31 32 6. $32,000, money earns 6% compounded quarterly, 3 years 34 7. $78,500, money earns 6% compounded semiannually, 5 years 7. 35 8. $29,804, money earns 12% compounded monthly, 2 years 8. 9. Explain the difference between a sinking fund (see Objective 1) and the present value of an to bas art on babeon annuity discussed in Section 11.2. showogno Page 427 Question 4 Prabeat off C/ indicates an exercise that is related to the Case in Point feature.428 CHAPTER 11 Annuities, Stocks, and Bonds 10. What is a sinking fund table? Who would use one? (See Objective 2.) Solve each application problem. 11. STUDENT UNION A college needs $920,000 in 3 years to remodel the student union. (a) It decides to make payments into a sinking fund at the end of each semiannual period. (a) Find the amount of each payment, assuming 5% per year compounded semiannually. (b) (b) Find the total interest earned. (a) Payment = $920,000 X .15655 = $144,026 (b) Interest = $920,000 - (6 X $144,026) = $55,844 12. SCUBA DIVING The owner of Emerald Diving (a plans to buy all new scuba diving equipment to (b rent to divers in 5 years at a cost of $122,300. He believes that he can earn 4% compounded quarterly. Find (a) the amount of each of the quarterly payments needed and (b) the total interest earned. Page 428 Question 10 13. ACCUMULATING $1,000,000 Kyle Anderson is 25 years old and wants to accumulate $1,000,000 by the time he is 60. He believes he can earn 8% per year by investing in stocks and bonds. Find (a) the amount of the annual payment needed and (b) the total interest earned. 14. ALLIGATOR HUNTING Cajun Jack needs $45,000 in 4 years for boats used to hunt alligators. (a) Find the amount of each payment if payments are made at the end of each quarter with interest at 6% compounded quarterly. (b) Find the total amount of interest earned.3000 430 CHAPTER 11 Annuities, Stocks, and Bonds 22. COMMERCIAL BUILDING Jeremy Painter plans to make a down payment of $70,000 on a commercial building for his plumbing company in 5 years. Construct a sinking fund table given semiannual payments of $6106.10 at the end of each period and an interest rate of 6% compounded semiannually. Payment Amount of Interest Total in Number Deposit Earned Account Page 430 Question 22 Agubas ted 23. SAVING FOR COLLEGE Barbara Funicello hopes to go to a private college where tuition 23. is $22,500 per year. She believes that tuition will increase at 8% for the 4 years until she plans to enter college. Find the end-of-quarter payments needed to accumulate funds to pay the first year's tuition if funds earn 6% compounded quarterly. Round to the nearest dollar at each step. 24. FIRE TRUCK A volunteer fire department anticipates purchasing a fire engine in 3 years. 24. Today it would cost $625,000, but the cost is increasing at 4% per year. Find the semian- nual payments needed to accumulate funds to purchase the truck if funds earn 6% com- pounded semiannually. Round to the nearest dollar at each step. 25. NEW ROOF The manager of an apartment complex estimates she will need a new roof on one building in 5 years. Today it would cost $52,000 to reroof the building, but the cost isand (c) compare the two investments. whether she should invest her retirement monies in certificates of a mutual fund containing stock. Assume payments of $2000 per year for 30 years and (a) a certificate of deposit paying 4% compounded annually or (b) a mutual fund that tracks the Standard and Poor's 500 and has returned 8% per year. Find the future value for both SOLUTION / Quick TIP positive investment returns on stocks are not guaranteed. How - ever, stocks usually return more (a) Use 4% per year and 30 years in the table in Section 1 1.1 to find 56.08494. than bank accounts over long Future value = $2000 x 56.08494 = $112,169.88 periods of time. (b) Use 8% per year and 30 years in the table in Section 1 1.1 to find 113.28321. Future value = $2000 X 113.28321 = $226,566.42 (c) Difference = $226,566.42 - $112,169.88 = $114,396.54 Stocks yield more but have higher risk. Cynthia Peck will need to decide how much risk s will accept before making a decision. QUICK CHECK 5 The owner of Termites Inc. plans to deposit $15,000 at the end of each year for 10 yea into an investment account. One investment would pay 5% per year, and he assumes fund would continue to yield 10% per year. Find the future value of both. ORAL STOCKS 11.4 Exercises // MyLab Math The shaded sections below contain solutions to help you get a QUICK START on the various types of exercises. Find the following from the stock table on pages 435-436. (See Example 1.) 1. Low for the year for Bankrate (RATE) 1. $6.59 2. High for the year for Bard CR (BCR) 2. $239.43 3. Most recent dividend for Barnes&Noble (BKS) 4. Most recent dividend for Bank of Hawaii (BOH) 5. Volume for Bladex (BLX) 6. Volume for BarracudaNtwks (CUDA) 7. PE ratio for BT Group (BT) Page 439 8. PE ratio for BankofButterfield (NTB) Question 4 8. 9. Estimated earnings per share for this year for Barrick Gold (ABX) 9 . 10. 10. Estimated earnings per share for this year for Bank of Hawaii (BOH)440 CHAPTER 11 Annuities, Stocks, and Bonds 11. 11. Dividend yield for BankNY Mellon (BK) 12. 12. Dividend yield for Baker Hughes (BHD) 13 . Find 13. Estimated earnings next year for BP (BP) 14. see 14. Estimated earnings next year for BadgerMeter (BMI) 15. 15. Change from previous week for BanColumbia (CIB) 16. 16. Change from previous week for Babcock& Wilcox (BW) 33 . 17 . 17. Closing price for the week for BRF (BRFS) 18. 34 . 18. Closing price for the week for BancoSantander (SAN) Ignore commissions and find the cost for the following stock purchases at the closing price for 35 the week. Then find the annual dividend that will be paid on those shares. Stock Cost Dividend 36 Number of Shares $544 19. Baker Hughes (BHI) 800 $53, 112 800 X $66.39 = $53, 112; 800 X $.17 X 4 = $544 20. Barnes & Noble (BKS) 200 21. Barclays (BCS) bang . It noise 500 22. Barrick Gold (ABX) 100 23. Bank of Nova Scotia (BNS) OOOS ISIR 24. British Petroleum (BP)300 25. Explain corporations, shares, and shareholders. (See Objective 1.) 26. Use the chart of the Dow Jones Industrial Average and estimate the years in which stocks Page 440 fell by more than 10%. (See Objective 5.) Questions Find the current yield for each of the following stocks. Round to the nearest tenth of a percent. 18, 22 and (See Example 3.) Current Price Annual Current Stock per Share Dividend Yield 30 27. Coca-cola (KO) $41.60 $1.40 $1.40 = $41.60 = 3.4% 3.4% 28. Facebook (FB) $117.27 $0 29. Mcdonald's (MCD) $123.14 $3.76 30. Apple Inc. (AAPL) $116.52 $2.28 31. Nike (NKE) $51.91 $.72 32. Walmart (WMT) $69.54 $2.00(See Example 4.) Find the PE ratio for each of the following. Round all answers to the nearest whole number. 11.4 Exercises Current Price 441 per Share Annual Net Stock Earnings per Share 33. Coca-cola (KO) $41.60 $1.65 PE Ratio $41.60 = $1.65 = 25 25 34. Facebook (FB) $117.27 $2.09 35. Mcdonald's (MCD) $123.14 $5.32 36. Apple Inc. (AAPL) $116.52 $8.31 Page 441 37. Nike (NKE) $51.91 $2.22 38. Walmart (WMT) $69.54 $4.61 Questions Stock prices on consecutive days for a stock are shown next. Find the increase (decrease) in the 36 & 42 price of each stock as a number and the percent increase (decrease) rounded to the nearest tenth of a percent. 39. $34.35, 35.20 40. $46.50, 45.90 Solve the following application problems. 41. STOCK PURCHASE Patsy Bonner buys 200 shares of Target at $56.30 and 100 shares of 41. $18, 133 Pepsico at $68.73. Find the total cost ignoring commissions. 200 X $56.30 + 100 X $68.73 = $18, 133 42. WRITING A WILL In her will, Barbara Bains stated that the trustee should purchase 300 42. shares of Mcdonald's and 200 shares of Walmart and give the stock to her grandson on his 25th birthday. If the stocks are selling for $87.91 per share and $72.02 per share, respec- tively, find the total amount paid, ignoring broker's commissions. 13. CDS OR GLOBAL STOCKS Stan Walker is comparing CDs currently yielding 2% (a) compounded semiannually to a mutual fund with stocks that he believes will yield 8% compounded semiannually. Find the future value of an annuity with deposits of $600 every 6 months for 10 years for (a) the CDs and (b) the mutual fund. (c) Find the difference.terest rate of a (a) Use the formula for simple interest: 1 = PRT. 11.5 Exercises is the last yield 447 as by the total maturity value Interest = $50,000 x .065 = $3250 (b) Again use the formula for simple interest, but now the principal (P) is unknown. Divide both sides of I = PRT by RT to find the following form of the equation. nz Foods Co Principal = P = $10,000 QUICK CHECK 5 RT 065 X 1 = $153,846.15 James Corporation wants $80,000 per year in interest. Find the amount the firm must invest in a bond fund yielding 6.125% to attain this annual income. 11.5 Exercises MyLab Math me shaded sections below contain solutions to help you get a QUICK START on the various types of exercises. use the bond table on page 445 to find the following for Anheuser-Busch Inbev Finance (ABIBB) maturing 2046. (See Examples 1 and 2.) 1 . Price per bond 2. Volume of bonds sold during the week 1. $1054.09 3. Date when bonds must be paid off by Anheuser- 2. Busch turing 4. Annual interest paid 5. Last yield or yield to maturity 4. 6. Price to buy 50 of these bonds, including sales 5. charge of $1 per bond 6. Assume a Find the cost, including sales charges of $1 per bond, for each of the following purchases. bonds (See Example 3.) Number Bond Maturity Purchased Cost 7. Noble Holding Int. Ltd (NE) Jan. 15, 2024 20 $19,482.60 ($973.13 + $1) X 20 bonds = $19, 482.60 8. Deutsche Bank Ag (DB) Oct. 4, 2021 50 9. Teva Pharmaceutical (TEVA) Oct. 1, 2026 100 10. Unitedhealth Group (UNH) Jan. 15, 2027 80 11. Ensco Int. (ESV) Mar. 15, 2021 30 12. JPMorgan Chase (JPM) Oct. 1, 2026 200 13. What are bonds and why are they used? (See Objectives 1 and 2.) Page 447 Ul indicates an exercise that is related to the Case in Point feature. Questions 4 & 12448 CHAPTER 11 Annuities, Stocks, and Bonds 14. Explain how a bondholder can estimate the effective interest rate or the total cost of the investment, including commissions. (See Example 3.) Page 448 Question 18 Solve each application problem. Assume a sales commission of $1 per bond, unless indicate otherwise, and use the table on page on page 445. Round the rate to the nearest tenth of a percent. 15. BOND FUND Pete Chong manages bonds for a fund company. He purchases 4000 Act- (a) avis Funding Scs (AGN) bonds that mature in 2045. Since this is a large purchase, the commission is only $0.20 per bond. Find (a) the total cost of the purchase including com- (b) missions, (b) the annual interest, and (c) the effective interest rate based on total cost (c) including commissions. (a) Total cost = ($967.91 + $.20) X 4000 = $3,872, 440 (b) Annual interest = (.0475 X $1000) X 4000 = $190,000 (c) Effective interest rate = $190,000 = $3,872,440 = 4.9% 16. BOND PURCHASE New York purchased 10,000 bonds issued by Citigroup (C) bonds (a) maturing in 2021. The commission is $.20 per bond due to the large volume. Find (a) the total cost including commissions, (b) the annual interest and (c) the effective interest rate. (b ) (c) 17. BOND PURCHASE Charles Smitten needed more income than offered by money market (a) funds, so he purchased 25 Oracle (ORCL) bonds maturing in 2021. Find (a) the total cost including commissions, (b) the annual interest and (c) the effective interest rate. (b ) (c) 18. RETIREMENT FUNDS United Worker's pension administrator purchased 90 Apple (AAPL) bonds maturing in 2046. Find (a) the total cost including commissions, (b) the (a) annual interest and (c) the effective interest rate. (b ) (c) 19. BOND FUND Bernice Clarence places $45,000 in a bond fund that is currently yielding 8% compounded annually. (a) Find interest for the first year. (b) She decides to let all (a) interest payments remain in the account. Find the amount in the account after 10 years if (b) the fund continues to earn 8% compounded annually. / 20. BOND FUND The hospital where Darnell Johnson works has an endowment funded by alumni and business owners in the community. The manager of the endowment invested (a) $500,000 in a bond fund yielding 6% compounded semiannually. Find (a) the interest for the first year and (b) the future value of the account in 8 years. (b). laiting on discussion 414 CHAPTER 11 Annuities, Stocks, and Bonds 11.1 Exercises Page 414 MyLa The shaded sections below contain solutions to help you get a QUICK Questions 6, Find the amount of the following ordinary annuities, then find the intosod. & 14 (See Examples ] and 2.) Amount of Each Deposit Time Amount of Interest Deposited Rate ( Years) Annuity Earned 1. $900 annually 5% 18 $25,319.14 $9119.14 2. $2900 $900 X 28.13238 = $25,319.14; / = $25,319.14 - (18 X $900) = $9119.14 annually 8% $17,013.14 $2513.14 $2900 X 5.86660 = $17,013.14; / = $17,013.14 - (5 X $2900) = $2513.14 3. $7500 semiannually 6% 10 4. $9200 semiannually 8% 5 5. $3500 quarterly 10% 7 6. $6900 quarterly 4% 4 Find the amount of the following annuities DUE, then find the interest earned. (See Example 3.) Amount of Tim Amount of Interest Each Deposit Deposited Rate (Years) Annuity Earned 7. $1200 annually 8% $7603.12 $1603.12 Look up 8%, 5 + 1 = 6 periods, finding 7.33593. $1200 X 7.33593 - $1200 = $7603.12 Interest = $7603.12 - 5 X $1200 = $1603.12 8. $400 annually 6% $2957.54 $557.54 Look up 6%, 6 + 1 = 7 periods, finding 8.39384. $400 X 8.39384 - $400 = $2957.54 Interest = $2957.54 - 6 X $400 = $557.54 9. $9500 semiannually 4% 10. $1800 semiannually 5% 6 11. $3800 quarterly 8% W quarterly 10% 5 12. $10,200 1 1 13. Explain the difference between an annuity and an annuity due. (See Objectives 2 and 3.) 14. Describe the differences between an IRA, a 401(k), and a 403(b). (See Objective 4.)