Section 11.6 Ordinary Annuities, Sinking Funds, and Retirement Investments

1. Section 11.6Ordinary Annuities, Sinking Funds, and Retirement Investments

2. What You Will Learn • Ordinary Annuities • Sinking Funds • Variable Annuities • Immediate Annuities • IRA’s • 401ks and 403bs

3. Annuity • An annuity is an account into which, or out of which, a sequence of scheduled payments is made.

4. Ordinary Annuity • An annuity into which equal payments are made at regular intervals, with the interest compounded at the end of each interval and with a fixed interest rate for each compounding period, is called an ordinary annuity or fixed annuity.

5. Ordinary Annuity • The amount of money that is present in an ordinary annuity after t years is known as theaccumulated amount or thefuture value of an annuity. • To determine the accumulated amount of an ordinary annuity, we could use a computer to generate a spreadsheet, as on the next slide.

6. Ordinary Annuity1st half of table

7. Ordinary Annuity2nd half of table

8. Ordinary Annuity • Another way, and perhaps a more efficient way, to calculate the accumulated amount in an ordinary annuity is to use the ordinary annuity formula on the next slide.

9. Ordinary Annuity Formula • The accumulated amount, A, of an ordinary annuity with payments of p dollars made n times per year, for t years, at interest rate, r, compounded at the end of each payment period is given by the formula

10. Example 1: Using the Ordinary Annuity Formula Bill and Megan Lutes are depositing $250 each quarter in an ordinary annuity that pays 4% interest compounded quarterly. Determine the accumulated amount in this annuity after 35 years.

11. Example 1: Using the Ordinary Annuity Formula • Solution • p = $250, r = 0.04, n = 4, t = 35.

12. Example 1: Using the Ordinary Annuity Formula • There will be about $75,677.48 in Bill and Megan’s annuity after 35 years.

13. Timely Tip • An ordinary annuity is used when you wish to determine the accumulated amount obtained over n years when you contribute a fixed amount each period. A sinking fund is used when you wish to determine how much money an investor must invest each period to reach an accumulated amount at a specific time.

14. Sinking Fund • A sinking fund is a type of annuity in which the goal is to save a specific amount of money in a specific amount of time.

15. Sinking Fund Payment Formula • In the formula, p is the payment needed to reach the accumulated amount, A. Payments are made n times per year, for t years, into a sinking fund with interest rate r, compounded n times per year.

16. Example 2: Using Sinking Fund Payment Formula • Abigail and John Clayton would like to have $55,000 in 10 years to remodel their home. The Claytons decide to invest monthly in a sinking fund that pays 3.3% interest compounded monthly. How much should the Claytons invest in the sinking fund each month to accumulate $55,000 in 10 years?

17. Example 2: Using Sinking Fund Payment Formula • Solution • A = $55,000, r = 0.033, n = 12, t = 10

18. Example 2: Using Sinking Fund Payment Formula • Solution • We often round to the nearest cent, or in this case, to $387.48. However, because $387.48 is slightly less than the answer we obtained, we will round our answer up to $387.49 to ensure that the Claytons reach their goal of $55,000.

19. Variable Annuities • A variable annuity is an annuity that is invested in stocks, bonds, mutual funds, or other investments that do not provide a guaranteed interest rate. • The term variable is used because the value of the annuity will vary depending on the performance of the investment options chosen by the investor.

20. Variable Annuities • Like an ordinary annuity, an investor usually invests in a variable annuity by making regular periodic payments. • Unlike an ordinary annuity, however, a variable annuity does not have a fixed rate of interest.

21. Immediate Annuities • An immediate annuity is an annuity that is established with a lump sum of money for the purpose of providing the investor with regular, usually monthly, payments for the rest of the investor’s life. In exchange for giving the investment company a lump sum of money, the investor is guaranteed to receive a monthly income for the duration of the investor’s life.

22. Individual Retirement Accounts • Individual retirement accounts, also known as IRAs, are savings accounts that allow individuals to invest up to a certain amount of money each year for the purpose of saving for retirement. • IRAs have distinct tax advantages over ordinary savings accounts. There are several different kinds of IRAs, but most can be classified as either a traditional IRA or a Roth IRA.

23. Individual Retirement Accounts • A traditional IRA is an IRA into which pretax money is invested, meaning that any money invested into a traditional IRA is not subject to income taxes. However, when money is withdrawn from a traditional IRA, the money is subject to income taxes.

24. Individual Retirement Accounts • A Roth IRA is an IRA into which post tax money is invested, meaning that the investor has already paid income taxes on the money invested. When money is withdrawn from a Roth IRA after the investor reaches retirement age, the money is not subject to income taxes.

25. 401ks • A 401k plan is a retirement savings plan that allows employees of private companies to make contributions of pre-income tax dollars that are then pooled with other employees’ money. • These funds are then invested in a variety of stocks, bonds, money markets, and mutual funds.

26. 401ks • Although 401k plans share many of the same tax advantages as IRAs, they also have several distinct advantages.

27. 401ks • First, employees are generally allowed to invest more money annually in a 401k plan than in an IRA. Often, employees are eligible to invest up to 15% of their annual income into a 401k plan. • A second advantage is that some employers will match employee contributions up to a certain limit.

28. 401ks • A Roth 401k plan is a retirement savings plan that differs from a 401k plan 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.

29. 403bs • 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-for-profit 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.

30. 403bs • Rather, a 403b plan is frequently established independently by the employee with a representative of an investment or insurance company.

31. Summary • 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 Web site.

32. Summary • Regardless of the source of your information, it is very important to do your own research and ask many questions prior to investing.