10.6 Ordinary Annuities, Sinking Funds, and Retirement Investments 645 Next we will study a specific type of annuity called a sinking fund . Microsoft Excel Read the Technology Tip on page 608. To determine the accumulated amount using Excel, place the letters p r n t , , , , and A in cells A1 through E1, respectively. In cells A2 through D2, place the values for p r n , , , and t, respectively. In cell E2, use the formula box to add the formula = + − (A2 * ((1 B2/C2) ^ (C2 * D2) 1))/(B2/C2) After the Enter key is pressed, the result is as follows. 1 A B C D E 2 3 p r n t A 250 0.04 4 35 75677.48042 Sheet2 Ready Sheet3 Sheet1 Did You Know? Investing in Mutual Funds A mutual fund is an investment tool that enables investors to indirectly own a wide variety of stocks, bonds, or other investments. When investors purchase shares in a mutual fund, they are actually placing their money in a pool along with many other investors. The investments within a mutual fund are called the mutual fund’s portfolio . The investors of a mutual fund share the gains and losses from the investments within the portfolio. There are some distinct advantages to investing in mutual funds rather than investing in individual stocks and bonds. First, investors in mutual funds have their money managed by full-time professionals. Second, because large sums of money are managed within a mutual fund, costs related to investing, known as commissions , are generally lower than they are for purchasing individual stocks and bonds. Third, when investors purchase shares in a mutual fund, they are indirectly purchasing shares in a multitude of stocks or bonds. This diversification can greatly help to reduce some of the risks of investing. One disadvantage of mutual fund investing is the potential to miss out on a large return on investment. In general, though, investing in mutual funds is considered an excellent way to begin investing and to maintain diverse ownership in a variety of investments. Sinking Funds We now return to the second question asked at the beginning of this section. Recall that the Weismans have a goal of saving $50,000 in 10 years for their child’s college education and want to know how much they should begin to invest each month in an account paying a 6% interest rate compounded monthly. The Weismans can help reach this goal by investing in a special kind of annuity called a sinking fund . Definition: 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. Many types of sinking funds are used for many different purposes by individuals, corporations, and governments. Historically, sinking funds were used by governments to set aside money to pay off bonds that were used to borrow large sums of money for major civic projects such as sewers, roads, or bridges. The term sinking fund referred to the sinking of the debt that was owed to repay the bonds. Our discussion of sinking funds will focus on answering questions similar to the question facing the Weismans. Because they are interested in saving a specific amount of money, $50,000, in a specific amount of time, 10 years, their investment can be considered a sinking fund. 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. To determine the amount of money to be invested in a sinking fund, we can solve the ordinary annuity formula for the payment, p. Solving this formula for p gives us the following formula. Sinking Fund Payment Formula p A r n r n 1 1 n t ( ) = ⎛ ⎝ ⎞ ⎠ ⎛ + ⎝ ⎞ ⎠ − ⋅ 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 as a decimal number, compounded n times per year.
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