608 CHAPTER 10 Consumer Mathematics Compound interest Example 2 Calculating Compound Interest Calculate the interest on $750 at 4% compounded semiannually for 8 years, using the compound interest formula. Solution Since the interest is compounded semiannually, there are two periods per year. Thus, n 2, = r 0.04, = and t 8. = Substituting into the formula, we can determine the accumulated amount in the account, A. A p r n 1 750 1 0.04 2 750(1.02) 750(1.3727857) 1029.59 n t ( ) (2 8) 16 = ⎛ + ⎝ ⎞ ⎠ = ⎛ + ⎝ ⎞ ⎠ = ≈ ≈ ⋅ ⋅ Since the accumulated amount is $1029.59 and the original principal is $750, the interest is the difference, $1029.59 $750, − or $279.59. 7 Now try Exercise 5 TECHNOLOGY TIP Scientific Calculator There are various ways to determine compound interest using a scientific calculator. In Example 1, we had to evaluate 3000 1 0.018 12 (122) + ⎛ ⎝⎜ ⎞ ⎠⎟ ⋅ To evaluate this expression on a scientific calculator, enter the following keys. y 3000 ( 1 0.018 12 ) ( 12 2 ) x × + ÷ × = After the = key is pressed, the answer 3109.883655 is displayed. This answer checks with the answer obtained in Example 1. Note that a scientific calculator will automatically apply the order of operations discussed in Section 6.1. Microsoft Excel The software program Excel can also be used to determine compound interest. Excel is a spreadsheet, so once you insert a formula, you can change the value of the variables and the new answer will be automatically displayed. If you are not familiar with Excel, you can get help at Support.Microsoft.com. To use Excel to determine the compound interest, set up the following columns. Then, to set up the formula in cell E2, go to the formula bar on top and enter A2*(1 B2/C2) ^ (C2*D2) = + Then press the Enter key. The answer, 3109.883655, will appear in cell E2. Suppose you now wanted to determine the compound interest for p r 6000, 0.05, = = n 24, = and t 6. = If you were to change the values in cells A2 through D2 to these values respectively, the new answer, 8096.625764, would be displayed in cell E2. 1 A B C D E 2 3 p r n t A 3000 0.018 12 2 Sheet2 Ready Sheet3 Sheet1 Did You Know? Federal Reserve Banks Varga Jozsef Zoltan/ Shutterstock Rabanser/Shutterstock Federal Reserve Banks are institutions owned by commercial banks in the district they serve. The many functions performed by these banks include the following: clearing checks, issuing new currency, retiring damaged currency, making discount loans to banks within their districts, examining member state banks, collecting data on local business conditions, and conducting research to help establish monetary policy, including the setting of the discount interest rate used when banks borrow money from each other. Currently, there are Federal Reserve Banks in Boston, New York, Philadelphia, Richmond, Cleveland, Atlanta, Chicago, St. Louis, Minneapolis, Kansas City, Dallas, and San Francisco. Take a look at any dollar bill and you will see a circular symbol with the location of the Federal Reserve Bank that issued the bill.
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