Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Applications for the Management, Life, and Social Sciences
11th Edition
ISBN: 9781305108042
Author: Ronald J. Harshbarger, James J. Reynolds
Publisher: Cengage Learning
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 6.3, Problem 45E

Problems 41-44 are complex financial problems that require several skills, perhaps some from previous sections.

A small business owner contributes $3000 at the end of each quarter to a retirement account that earns 8% compounded quarterly.

(a) How long will it be until the account is worth $150,000?

(b) Suppose when the account reaches $150,000, the business owner increases the contributions to $5000 at the end of each quarter. What will the total value of the account be after 15 more years?

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Chapter 6 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 6.1 - CHECKPOINT 1. What is the simple interest...Ch. 6.1 - CHECKPOINT 2. If $8000 is invested at 6% simple...Ch. 6.1 - CHECKPOINT 3. If a $2500 investment grows to $2875...Ch. 6.1 - Prob. 4CPCh. 6.1 - CHECKPOINT 5. Given the arithmetic sequence...Ch. 6.1 - Prob. 1ECh. 6.1 - SIMPLE INTEREST In Problems 1-4, find the...Ch. 6.1 - SIMPLE INTEREST In Problems 1-4, find the...Ch. 6.1 - Prob. 4ECh. 6.1 - 3. $10,000 is invested for 6 years at an annual...
Ch. 6.1 - 4. $800 is invested for 5 years at an annual...Ch. 6.1 - $1000 is invested for 3 months at an annual simple...Ch. 6.1 - 6. $1800 is invested for 9 months at an annual...Ch. 6.1 - If you borrow $800 for 6 months at 16% annual...Ch. 6.1 - 8. If you borrow $1600 for 2 years at annual...Ch. 6.1 - 9. If you lend $3500 to a friend for 15 months at ...Ch. 6.1 - 10. Mrs. Gonzalez lent $2500 to her son Luis for 7...Ch. 6.1 - A couple bought some stock for $30 per share that...Ch. 6.1 - Jenny Reed bought SSX stock for $16 per share. The...Ch. 6.1 - 13. (a) To buy a Treasury bill (T-bill) that...Ch. 6.1 - 14. Janie Christopher lent $6000 to a friend for...Ch. 6.1 - A firm buys 12 file cabinets at $140 each, with...Ch. 6.1 - 16. A student has a savings account earning 9%...Ch. 6.1 - If you want to earn 15% annual simple interest on...Ch. 6.1 - 18. What is the present value of an investment at...Ch. 6.1 - 19. If $5000 is invested at 8% annual simple...Ch. 6.1 - 20. How long does it take for $8500 invested at...Ch. 6.1 - 21. A retailer owes a wholesaler $500,000 due in...Ch. 6.1 - 22. An investor owns several apartment buildings....Ch. 6.1 - 23. Bill Casler bought a $2000,9-month certificate...Ch. 6.1 - 24. Suppose you lent $5000 to friend 1 for 18...Ch. 6.1 - 25. Write the first ten terms of the sequence...Ch. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - 29. Write the first four terms and the 10th term...Ch. 6.1 - Prob. 32ECh. 6.1 - In Problems 31-34, (a) identify d and and (b)...Ch. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - 35. Find the 83rd term of the arithmetic sequence...Ch. 6.1 - 36. Find the 66th term of the arithmetic sequence...Ch. 6.1 - 37. Find the 100th term of the arithmetic sequence...Ch. 6.1 - 38. Find the 73rd term of the arithmetic sequence...Ch. 6.1 - 39. Find the sum of the first 38 terms of the...Ch. 6.1 - 40. Find the sum of the first 56 terms of the...Ch. 6.1 - 41. Find the sum of the first 70 terms of the...Ch. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - 46. Salaries Suppose you are offered a job with a...Ch. 6.1 - 47. Profit A new firm loses $4000 in its first...Ch. 6.1 - 48. Pay raises If you make $36,000 and get $2400...Ch. 6.1 - 49. Salaries Suppose you are offered two identical...Ch. 6.1 - 50. Profit A new firm loses $4000 in its first...Ch. 6.1 - 51. Pay raises If you are an employee, would you...Ch. 6.1 - Prob. 54ECh. 6.2 - CHECKPOINT 1. If $5000 is invested at compounded...Ch. 6.2 - CHECKPOINT 2. Find the present value of an...Ch. 6.2 - CHECKPOINT 3. For each future value formula below,...Ch. 6.2 - CHECKPOINT 4. If $5000 is invested at 6%...Ch. 6.2 - CHECKPOINT 5. Find the annual percentage yield of...Ch. 6.2 - CHECKPOINT 6. How long does it take $5000 to...Ch. 6.2 - CHECKPOINT 7. Identify any geometric sequences...Ch. 6.2 - CHECKPOINT 8. (a) Find the 40th term of the...Ch. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3ECh. 6.2 - COMPOUND INTEREST In Problems 1-4, find the...Ch. 6.2 - For each investment situation in Problems 3-6,...Ch. 6.2 - For each investment situation in Problems 3-6,...Ch. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - 7. Find the future value if $8000 is invested for...Ch. 6.2 - 8. What is the future value if $8600 is invested...Ch. 6.2 - 9. What are the future value and the interest...Ch. 6.2 - 10. What interest will be earned if $6300 is...Ch. 6.2 - 11. What lump sum do parents need to deposit in an...Ch. 6.2 - 12. What lump sum should be deposited in an...Ch. 6.2 - 13. What present value amounts to $10,000 if it is...Ch. 6.2 - 14. What present value amounts to $300,000 if it...Ch. 6.2 - 15. Find the future value if $5100 is invested for...Ch. 6.2 - 16. Find the interest that will result if $8000 is...Ch. 6.2 - 17. What is the compound interest if $41,000 is...Ch. 6.2 - 18. If $8000 is invested at compounded...Ch. 6.2 - 19. Grandparents want to make a gift of $100,000...Ch. 6.2 - 20. Suppose an individual wants to have $200,000...Ch. 6.2 - 21. Which investment will earn more money, a $1000...Ch. 6.2 - Prob. 24ECh. 6.2 - 23. Find the annual percentage yield for an...Ch. 6.2 - Prob. 26ECh. 6.2 - In Problems 25 and 26, rank each interest rate and...Ch. 6.2 - Prob. 28ECh. 6.2 - 27. Two different investment companies offer...Ch. 6.2 - 28. For life insurance policies, some of the...Ch. 6.2 - 29. The figure shows a graph of the future value...Ch. 6.2 - Prob. 32ECh. 6.2 - 31. Microsoft's stock price peaked at of its IPO...Ch. 6.2 - If $10,000 had been invested in the Sagamore...Ch. 6.2 - 33. How long (in years) would $700 have to be...Ch. 6.2 - 34. How long (in years) would $600 have to be...Ch. 6.2 - 35. At what nominal rate compounded quarterly...Ch. 6.2 - 36. At what nominal rate compounded annually would...Ch. 6.2 - 37. For her 1st birthday, Ruth’s grandparents...Ch. 6.2 - 38. To help their son buy a car on his 16th...Ch. 6.2 - 39. (a) A 40-year-old man has $432,860 in an IRA...Ch. 6.2 - 40. (a) The purchase of Alaska cost the United...Ch. 6.2 - 41. A couple needs $45,000 as a down payment for a...Ch. 6.2 - 42. How long does it take an account containing...Ch. 6.2 - 43. Mary Stahley invested $2500 in a 36-month...Ch. 6.2 - 44. Suppose Patrick Goldsmith deposited $1000 in...Ch. 6.2 - In Problems 45 and 46, use a spreadsheet or...Ch. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - In Problems 49-58, write an expression that gives...Ch. 6.2 - In Problems 49-58, write an expression that gives...Ch. 6.2 - In Problems 49-58, write an expression that gives...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - In Problems 49-58, write an expression that gives...Ch. 6.2 - 59. Inflation A house that 20 years ago was worth...Ch. 6.2 - Prob. 62ECh. 6.2 - 61. Population growth Suppose a country has a...Ch. 6.2 - Prob. 64ECh. 6.2 - Prob. 65ECh. 6.2 - 64. Population If a population of 8 million begins...Ch. 6.2 - 65. Ball rebounding A ball is dropped from a...Ch. 6.2 - 66. Water pumping A pump removes of the water in...Ch. 6.2 - 67. Depreciation A machine is valued at $10,000....Ch. 6.2 - 68. Profit Suppose a new business makes a $1000...Ch. 6.2 - Prob. 71ECh. 6.2 - Prob. 72ECh. 6.2 - Prob. 73ECh. 6.2 - Prob. 74ECh. 6.2 - 73. Chain letters Suppose you receive a chain...Ch. 6.2 - Prob. 76ECh. 6.2 - Prob. 77ECh. 6.3 - CHECKPOINT 1. Suppose that $500 is deposited at...Ch. 6.3 - CHECKPOINT 2. A sinking fund of $100,000 is to be...Ch. 6.3 - CHECKPOINT 3. Suppose $100 is deposited at the...Ch. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - In Problems 1-4, find the requested value (to the...Ch. 6.3 - 3. The figure shows a graph that compares the...Ch. 6.3 - 4. The figure shows a graph that compares the...Ch. 6.3 - 5. Find the future value of an annuity of $1300...Ch. 6.3 - Prob. 8ECh. 6.3 - Find the future value of an ordinary annuity of...Ch. 6.3 - Prob. 10ECh. 6.3 - 9. The Weidmans want to save $40,000 in 2 years...Ch. 6.3 - 10. A sinking fund is established to discharge a...Ch. 6.3 - 11. If $2500 is deposited at the end of each...Ch. 6.3 - 12. If $4000 is deposited at the end of each half...Ch. 6.3 - 13. In this sections Application Preview, we...Ch. 6.3 - 14. (a) Patty Stacey deposits $2000 at the end of...Ch. 6.3 - 15. Find the future value of an annuity due of...Ch. 6.3 - 16. Find the future value of an annuity due of...Ch. 6.3 - 17. Find the future value of an annuity due of...Ch. 6.3 - A house is rented for $3600 per quarter, with each...Ch. 6.3 - 19. How much must be deposited at the beginning of...Ch. 6.3 - 20. What is the size of the payments that must be...Ch. 6.3 - 21. A company wants to have $800,000 for office...Ch. 6.3 - 22. Seana wants to save $20,000 toward the...Ch. 6.3 - In Problems 23-40, (a) state whether the problem...Ch. 6.3 - In Problems 23-40, (a) state whether the problem...Ch. 6.3 - Prob. 27ECh. 6.3 - In Problems 23-40, (a) state whether the problem...Ch. 6.3 - In Problems 23-40, (a) state whether the problem...Ch. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - 32. Sofia can deposit $350 at the beginning of...Ch. 6.3 - 33. Mr. Gordon plans to invest $300 at the end of...Ch. 6.3 - 34. For 3 years, $4000 is placed in a savings...Ch. 6.3 - 35. Grandparents plan to open an account on their...Ch. 6.3 - 36. How much money should a couple deposit at the...Ch. 6.3 - Prob. 39ECh. 6.3 - 38. A company establishes a sinking fund to...Ch. 6.3 - 39. A sinking fund is established by a working...Ch. 6.3 - 40. A property owner has several rental units and...Ch. 6.3 - Problems 41-44 are complex financial problems that...Ch. 6.3 - Problems 41-44 are complex financial problems that...Ch. 6.3 - Problems 41-44 are complex financial problems that...Ch. 6.3 - Problems 41-44 are complex financial problems that...Ch. 6.4 - CHECKPOINT 1. Suppose an annuity pays $2000 at the...Ch. 6.4 - CHECKPOINT 2. An inheritance of $400,000 will...Ch. 6.4 - Prob. 3CPCh. 6.4 - Prob. 4CPCh. 6.4 - Prob. 1ECh. 6.4 - In Problems 1-4, find the requested value (to the...Ch. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - 3. Find the present value of an annuity of $6000...Ch. 6.4 - 4. Find the present value of an annuity that pays...Ch. 6.4 - 5. Suppose a state lottery prize of $5 million is...Ch. 6.4 - 6. How much is needed in an account that earns...Ch. 6.4 - 7. With a present value of $135,000, what is the...Ch. 6.4 - 8. If $88,000 is invested in an annuity that earns...Ch. 6.4 - 9. A personal account earmarked as a retirement...Ch. 6.4 - 10. A professional athlete invested $2.5 million...Ch. 6.4 - 11. Suppose that a 25-year government bond has a...Ch. 6.4 - 12. Suppose that a 10-year corporate bond has a...Ch. 6.4 - 13. The figure shows a graph that compares the...Ch. 6.4 - 14. The figure shows a graph that compares the...Ch. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - 17. Find the present value of an annuity due that...Ch. 6.4 - 18. Find the present value of an annuity due that...Ch. 6.4 - 19. What amount must be set aside now to generate...Ch. 6.4 - 20. Suppose an annuity will pay $15,000 at the...Ch. 6.4 - 21. A year-end bonus of $25,000 will generate how...Ch. 6.4 - 22. A couple inherits $89,000. How much can this...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - Prob. 34ECh. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - Prob. 36ECh. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - In Problems 23-38, (a) decide whether the problem...Ch. 6.4 - 39. A 10-year Emmaco Corporate bond has a par...Ch. 6.4 - 40. Kodicom Inc. has 15-year bonds with a $5000...Ch. 6.4 - Problems 41-44 are complex financial problems that...Ch. 6.4 - Problems 41-44 are complex financial problems that...Ch. 6.4 - Problems 41-44 are complex financial problems that...Ch. 6.4 - Problems 41-44 are complex financial problems that...Ch. 6.4 - Prob. 47ECh. 6.4 - 46. Find the present value of an annuity of $2000...Ch. 6.4 - 47. The terms of a single parent’s will indicate...Ch. 6.4 - 48. On his 48th birthday, a man wants to set aside...Ch. 6.4 - 49. The semiannual tuition payment at a major...Ch. 6.4 - 50. A community is soliciting pledges for a...Ch. 6.4 - 51. Danny Metzger’s parents invested $ 1600 when...Ch. 6.4 - 52. Carol Goldsmith received a trust fund...Ch. 6.4 - Prob. 55ECh. 6.4 - 54. A couple received a $134,000 inheritance the...Ch. 6.5 - CHECKPOINT 1. A debt of $25,000 is to be amortized...Ch. 6.5 - CHECKPOINT 2. A new college graduate determines...Ch. 6.5 - Prob. 3CPCh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - 3. A debt of $8000 is to be amortized with 8 equal...Ch. 6.5 - 4. A loan of $10,000 is to be amortized with 10...Ch. 6.5 - 5. A recent graduate’s student loans total...Ch. 6.5 - 6. For equipment upgrades, a business borrowed...Ch. 6.5 - 7. A homeowner planning a kitchen remodeling can...Ch. 6.5 - 8. AdriAnne and Anna’s Auto Repair wants to add a...Ch. 6.5 - Prob. 9ECh. 6.5 - In Problems 9-12, develop an amortization schedule...Ch. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - 13. A $10,000 loan is to be amortized for 10 years...Ch. 6.5 - 14. A debt of $8000 is to be amortized with 8...Ch. 6.5 - 15. When Maria Acosta bought a car years ago, she...Ch. 6.5 - Prob. 16ECh. 6.5 - Problems 17-20 describe a debt to be amortized. In...Ch. 6.5 - Problems 17-20 describe a debt to be amortized. In...Ch. 6.5 - Problems 17-20 describe a debt to be amortized. In...Ch. 6.5 - Problems 17-20 describe a debt to be amortized. In...Ch. 6.5 - 21. A man buys a car for $36,000. If the interest...Ch. 6.5 - 22. A woman buys a car for $40,000. If the...Ch. 6.5 - 23. A couple purchasing a home budget $1800 per...Ch. 6.5 - 24. A developer wants to buy a certain parcel of...Ch. 6.5 - 25. A couple who borrow $90,000 for 30 years at...Ch. 6.5 - 26. A company that purchases a piece of equipment...Ch. 6.5 - 27. When Otto and Millie bought their home, they...Ch. 6.5 - Prob. 28ECh. 6.5 - A recent college graduate buys a new car by...Ch. 6.5 - A young couple buying their first home borrow...Ch. 6.5 - 31. Jadele, Inc., borrowed $12.8 million at 7.2%...Ch. 6.5 - 32. When Gustavo and Serrana bought their home,...Ch. 6.5 - Prob. 33ECh. 6.5 - Prob. 34ECh. 6.5 - Prob. 35ECh. 6.5 - 36. Some banks now have biweekly mortgages (that...Ch. 6.5 - Prob. 37ECh. 6.5 - 38. Time-share sales provide an opportunity for...Ch. 6.5 - COMBINED APPLICATIONS Problems 39 and 40 are...Ch. 6.5 - COMBINED APPLICATIONS Problems 39 and 40 are...Ch. 6 - 1. Find the first 4 terms of the sequence with nth...Ch. 6 - Prob. 2RECh. 6 - 3. Find the 80th term of the arithmetic sequence...Ch. 6 - 4. Find the 36th term of the arithmetic sequence...Ch. 6 - 5. Find the sum of the first 60 terms of the...Ch. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - 9. Loans If $8000 is borrowed at 12% simple...Ch. 6 - 10. Loan rate Mary Toy borrowed $2000 from her...Ch. 6 - 11. Tuition How much summer earnings must a...Ch. 6 - Prob. 12RECh. 6 - 13. Salaries Suppose you are offered two identical...Ch. 6 - Prob. 14RECh. 6 - Prob. 15RECh. 6 - Prob. 16RECh. 6 - 17. Interest If $1000 is invested for 4 years at...Ch. 6 - 18. Savings goal How much must one invest now to...Ch. 6 - Prob. 19RECh. 6 - 20. College fund A couple received an inheritance...Ch. 6 - Prob. 21RECh. 6 - 22. Investment rates (a) If an initial investment...Ch. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - 26. Annuity Find the future value of an ordinary...Ch. 6 - 27. Sinking fund How much would have to be...Ch. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - 33. Powerball lottery Winners of lotteries receive...Ch. 6 - 34. Payment from an annuity A recent college...Ch. 6 - 35. Payment from an annuity An IRA of $250,000 is...Ch. 6 - 36. Bond pricing Suppose that a 30-year municipal...Ch. 6 - 37. Duration of an annuity A retirement account...Ch. 6 - 38. Amortization A debt of $1000 with interest at...Ch. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - 41. Amortization schedule Complete the...Ch. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - 50. How much must be deposited at the end of each...Ch. 6 - Prob. 51RECh. 6 - 52. Quarterly payments of $500 are deposited in an...Ch. 6 - 53. If $8000 is invested at 7% compounded...Ch. 6 - 54. An investment broker bought some stock at...Ch. 6 - Prob. 55RECh. 6 - 56. A $5000 Mauranol, Inc., corporate bond matures...Ch. 6 - Prob. 57RECh. 6 - 58. A young couple receive an inheritance of...Ch. 6 - 59. A banker is trying to decide whether to...Ch. 6 - 60. To purchase a home, a couple borrowed $280,000...Ch. 6 - 61. A divorce settlement of $40,000 is paid in...Ch. 6 - 62. If $8000 is invested at 12% compounded...Ch. 6 - 63. A couple borrowed $ 184,000 to buy a...Ch. 6 - Problems 64-67 are complex financial problems that...Ch. 6 - Problems 64-67 are complex financial problems that...Ch. 6 - 1. If $8000 is invested at 7% compounded...Ch. 6 - 2. Suppose you invest $100 at the end of each...Ch. 6 - 3. To buy a municipal bond that matures to $10,000...Ch. 6 - 4. A debt of $280,000 is amortized with 40 equal...Ch. 6 - 5. If an investment of $1000 grew to $ 13,500 in 9...Ch. 6 - 6. A couple borrowed $97,000 at 7.2% compounded...Ch. 6 - 7. If you borrow $2500 for 15 months at 4% simple...Ch. 6 - 8. How much must you put aside at the beginning of...Ch. 6 - Prob. 9TCh. 6 - 10. An accountant wants to withdraw $3000 from an...Ch. 6 - Prob. 11TCh. 6 - Prob. 12TCh. 6 - 13. What amount must you invest in an account that...Ch. 6 - 14. If $1500 is deposited at the end of each...Ch. 6 - 15. Maxine deposited $400 at the beginning of each...Ch. 6 - 16. Grandparents plan to establish a college trust...Ch. 6 - Prob. 17TCh. 6 - 18. Suppose that a 10-year corporate bond has a...Ch. 6 - 19. The following sequence is arithmetic: 298.8,...Ch. 6 - Prob. 20TCh. 6 - 21. If you took a home mortgage loan of $150,000...Ch. 6 - 22. A couple would like to have $50,000 at the end...Ch. 6 - 23. A woman makes $3000 contributions at the end...
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