644 CHAPTER 10 Consumer Mathematics Did You Know? Investing in Bonds m Savings bonds A bond is a type of loan. When government agencies or corporations need money, they often borrow money from investors by selling, or issuing , bonds. When an investor purchases a bond, the investor is actually lending money to the bond’s issuer. The issuer agrees to pay the investor a certain interest rate over a stated period of time, usually from 1 to 30 years. The date on which the issuer repays the loan is called the maturity date . Although bonds are generally considered safer investments than stocks, they do have some risks. On rare occasions, issuers may fail to make interest payments or may fail to return the investment entirely. A more common risk is that the value of a bond may decrease if interest rates increase. Such a decrease may cause investors to lose some of their investment if they decide to sell their bond before the maturity date. In general, though, bonds offer a very stable investment that usually provide a higher return on investment than savings accounts or certificates of deposit without many of the risks associated with investing in stocks. Example 1 Using the Ordinary Annuity Formula Bill and Megan 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. Solution We will use the ordinary annuity formula. The payment, p, is $250, the interest rate, r, is 4% or 0.04, the account is compounded quarterly and the payments are made quarterly, so n is 4, and the number of years, t, is 35. We substitute these values into the formula to obtain the following. [ ] = ⎛ + ⎝ ⎞ ⎠ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎛ ⎝ ⎞ ⎠ = ⎛ + ⎝ ⎞ ⎠ − ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ ⎛ ⎝ ⎞ ⎠ = − ⎡⎣ ⎤⎦ ≈ − ≈ ≈ ≈ ⋅ ⋅ A p r n r n 1 1 250 1 0.04 4 1 0.04 4 250 1.01 1 0.01 250 4.027099 1 0.01 250(3.027099) 0.01 756.77475 0.01 75,677.475 n t ( ) (4 35) 140 Substitute the given values into the formula. To evaluate 1.01 , 140 we use the yx or the ^ key on a scientific calculator. We rounded 1.01140 to six decimal places. Thus, there will be about $75,677.48 in Bill and Megan’s annuity after 35 years. 7 Learning Catalytics Keyword: Angel-SOM-10.6 (See Preface for additional details.) Example 1 illustrated the power of establishing and maintaining a consistent investment plan and how using an ordinary annuity can help us save money. TECHNOLOGY TIP Scientific Calculator In Example 1, we determined the accumulated amount by evaluating the expression + ⎛ ⎝⎜ ⎞ ⎠⎟ − ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎛ ⎝⎜ ⎞ ⎠⎟ ⋅ 250 1 0.04 4 1 0.04 4 (4 35) There are various ways to evaluate this expression on a scientific calculator. One method is to press the following sequence of keys. y (250 ( (1 0.04 4) ( 4 35 ) 1 ) ) ( 0.04 4 ) x × + ÷ × − ÷ ÷ = After the = key is pressed, the answer 75677.48042 is displayed. ( Continued) Larry1235/Shutterstock
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