642 CHAPTER 10 Consumer Mathematics monthly, how much money will we accumulate after 30 years when we’re ready to retire? Also consider the Weismans, who are saving for their child’s college education. They might ask the question: If we know we will need $50,000 to send our child to college in 10 years, how much should we invest each month beginning now in an account paying a 6% interest rate compounded monthly? To answer these and similar questions, we will study two investments, the annuity and the sinking fund . Why This Is Important It’s never too early to start planning for retirement. In order to meet your retirement goals, you will want to make wise financial investments. Annuities and sinking funds are an important part of a long-term investment strategy. We begin this section with a discussion of annuities. Definition: Annuity An annuity is an account into which, or out of which, a sequence of scheduled payments is made. There are many different types of annuities. An annuity may be an investment account that you have with a bank, insurance company, or financial management firm. Annuities may contain investments in stocks, bonds, mutual funds, money market accounts, and other types of investments. Annuities are often used to save for longterm goals such as saving money for college or for retirement. An annuity can also be used to provide long-term regular payments to individuals. Lottery jackpots and professional athletes’ salaries are often paid out over time from annuities. Retirees may invest some of their retirement savings into an annuity and then receive monthly payments that come from that annuity. We will focus primarily on two basic types of annuities that are used as investment accounts, ordinary annuities and sinking funds . Later in this section, we will discuss other types of annuities. Ordinary Annuities Definition: 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 a fixed annuity . For example, the Brabsons, mentioned in the opening paragraph of this section, are asking a question that may involve an ordinary annuity. They plan to make $100 payments each month into an account that pays a 5% interest rate compounded monthly. With an ordinary annuity, the payment period and frequency of the compounding are the same, so the Brabsons make monthly payments and the interest is compounded monthly . They would like to know how much money would accumulate in this annuity after 30 years. The amount of money that is present in an ordinary annuity after t years is known as the accumulated amount or the future value of an annuity. Did You Know? Investing in Stocks When the owners of a company wish to raise money to expand their company, they often decide to sell part of the company to investors. When an investor purchases a portion of a company, the investor is said to own stock in the company. The unit of measure of the stock is called a share . By buying shares of stock, an investor is becoming a part owner, or shareholder , of the company. Large companies may have many millions or even billions of shares of stock available for trading to the general public. For example, in 2023, there were about 15.79 billion shares of Apple, Incorporated, owned by thousands of investors. On September 1, 2023 each of these shares was worth about $189.46. Investing in stocks over a long period of time is usually a good investment. However, since the price of stocks may go down as well as up, investing in stocks involves some risk of losing some or all of your investment. Neil Fraser/Alamy Stock Photo
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