648 CHAPTER 10 Consumer Mathematics in that an investor first pays income tax on the money used to invest in a Roth 401k plan. Like a Roth IRA, money withdrawn from a Roth 401k plan after the individual reaches retirement age is not subject to income tax. A 403b plan is a retirement plan similar to a 401k plan, but it is available only to employees of schools, civil governments, hospitals, charities, and other not-forprofit organizations. A 403b plan shares many of the same advantages as 401k plans. One major difference, though, is that a 403b plan is not necessarily established by the employer as is a 401k plan. Rather, a 403b plan is frequently established independently by the employee with a representative of an investment or insurance company. As you can see from this brief discussion of annuities, IRAs, 401k plans, and 403b plans, many important details can affect your decisions as you begin to invest for retirement. For more information, and for other types of retirement accounts not mentioned here, consult a financial advisor or visit a library or Internet website. Regardless of the source of your information, it is very important to do your own research and ask many questions prior to investing. Instructor Resources for Section 10.6 in MyLab Math • Objective-Level Videos 10.6 • PowerPoint Lecture Slides 10.6 • MyLab Exercises and Assignments 10.6 • Chapter 10 Projects Exercises $ All Exercises in this Section are related to financial literacy. Warm Up Exercises In Exercises 1–8, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. An account into which, or out of which, a sequence of scheduled payments is made, is called a(n) _______. Annuity 2. The amount of money that is present in an ordinary annuity after t years is known as the accumulated amount or the _______ value of the annuity. Future 3. A type of annuity in which the goal is to save a specific amount of money in a specific amount of time is called a(n) _______ fund. Sinking 4. A variable annuity is an annuity that is invested in stocks, bonds, mutual funds, or other investments that do not provide a(n) _______ interest rate. Guaranteed 5. An annuity that is established with a lump sum for the purpose of providing the investor with regular payments for the rest of the investor’s life is called a(n) _______ annuity. Immediate 6. Accounts in which individuals may invest up to a certain amount of money each year for the purpose of saving for retirement are called _______ retirement accounts. Individual 7. A retirement savings plan in which employees of private companies can make contributions of pre–income tax dollars that are then pooled with other employees’ money is called a(n) _______ plan. 401k 8. A retirement plan similar to a 401k plan, but available only to employees of schools, governments, and other not-forprofit organizations, is called a(n) _______ plan. 403b Practice the Skills In Exercises 9–12, use the ordinary annuity formula A p r n r n 1 1 n t ( ) = ⎛ + ⎝ ⎞ ⎠ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎛ ⎝ ⎞ ⎠ ⋅ to determine the accumulated amount in each annuity. Round all answers to the nearest cent. 9. $500 invested annually for 10 years at a 4.5% interest rate compounded annually $6144.10 10. $800 invested semiannually for 20 years at a 5% interest rate compounded semiannually $53,922.04 11. $400 invested quarterly for 35 years at a 8% interest rate compounded quarterly $299,929.32 12. $200 invested monthly for 40 years at a 6% interest rate compounded monthly $398,298.15 In Exercises 13–16, use the sinking fund formula p A r n r n 1 1 n t ( ) = ⎛ ⎝ ⎞ ⎠ ⎛ + ⎝ ⎞ ⎠ − ⋅ to determine the payment needed to reach the accumulated amount. To ensure that enough is invested each period, round each answer up to the next cent. 13. Semiannual payments with a 6% interest rate compounded semiannually for 10 years to accumulate $100,000 $3721.58 SECTION 10.6
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