10.3 Compound Interest 611 As we did in Example 4, when calculating the present value of an investment, we will always round our answers up to the nearest cent to ensure that we reach the desired accumulated amount. Did You Know? A Penny Saved . . . Example 4 Savings for College Will would like his daughter to attend college in 6 years when she finishes high school. Will would like to invest enough money in a certificate of deposit (CD) now to pay for his daughter’s college expenses. If Will estimates that he will need $30,000 in 6 years, how much should he invest now in a CD that has a rate of 4.56% compounded quarterly? Solution To answer this question, we will use the present value formula with A r n $30,000, 0.0456, 4, = = = and t 6. = p A r n 1 30,000 1 0.0456 4 30,000 (1.0114) 30,000 1.312655562 22,854.43407 n t ( ) (4 6) 24 = ⎛ + ⎝ ⎞ ⎠ = ⎛ + ⎝ ⎞ ⎠ = ≈ ≈ ⋅ ⋅ In most financial calculations,we round to the nearest cent, or in this case, to $22,854.43. However, because $22,854.43 is slightly less than the answer we obtained, we will round our answer up to $22,854.44 to ensure that Will reaches his goal. 7 Now try Exercise 39 TECHNOLOGY TIP Scientific Calculator To determine the present value in Example 4, we had to evaluate the expression + ⎛ ⎝⎜ ⎞ ⎠⎟ ⋅ 30,000 1 0.0456 4 (4 6) This expression can be evaluated on a scientific calculator as follows. y 30000 ( 1 0.0456 4 ) ( 4 6 ) x ÷ + ÷ × = After the = key is pressed, the answer 22854.43407 is displayed. This answer agrees with the answer obtained in Example 4. Excel Read the Technology Tip on compound interest on page 608. To determine the present value using Excel, enter A r n t , , , , and p in cells A1 through E1, respectively. In cells A2 through D2, enter the values of A r n , , , and t, respectively. When cell E2 is highlighted, in the formula box at the top, enter A2/(1 B2/C2)^(C2*D2) = + After the Enter key is pressed, the answer, 22854.43407, is displayed in cell E2. Excel also has many built-in financial functions, including Present Value (PV), Future Value (FV), and many others that are discussed in this section and chapter. Instructor Resources for Section 10.3 in MyLab Math • Objective-Level Videos 10.3 • Interactive Concept Video: Compound Interest • Animation: Compound Interest • PowerPoint Lecture Slides 10.3 • MyLab Exercises and Assignments 10.3 Library of Congress Prints and Photographs Division [LC-USZ62-25564]. Benjamin Franklin left 1000 pounds sterling (£) in his will to the city of Boston, where he was born. The money was to be lent to young apprentices who would pay 1 10 of the principal each year plus 5% interest compounded yearly. The money earned was to be used to benefit the inhabitants of Boston. By 1894, the fund’s value had increased to 90,000 £. Part of this legacy became the Benjamin Franklin Cummings Institute of Technology, a 2-year technical college founded in 1908.
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