646 CHAPTER 10 Consumer Mathematics As we did in Example 2, when calculating a sinking fund payment, we will round our final answers up to the nearest cent to ensure that we reach the desired accumulated amount in the sinking fund. In Example 2, we can check our answer by substituting $387.49 back into the ordinary annuity formula. Doing this calculation with a scientific calculator gives us an accumulated amount of about $55,000.79. If we substitute $387.48 for A into the ordinary annuity formula, the accumulated amount would be about $54,999.37, which is slightly short of the desired goal of $55,000. Example 2 Using the Sinking Fund Payment Formula The Burnettes would like to have $55,000 in 10 years, when they retire, to purchase a pontoon boat. The Burnettes decide to invest in a sinking fund that pays 3.3% interest compounded monthly. How much should the Burnettes invest each month in the sinking fund to accumulate $55,000 in 10 years? Solution Since we are looking for how much the Burnettes should invest each month to obtain an accumulated amount, we will use the sinking fund payment formula. The accumulated amount, A, is $55,000; the interest rate, r, is 3.3%, or 0.033; the payments are made monthly and the interest is compounded monthly, so n is 12; and the number of years, t, is 10. p A r n r n 1 1 55,000 0.033 12 1 0.033 12 1 151.25 0.39033827 387.48442 n t ( ) (1210) = ⎛ ⎝ ⎞ ⎠ ⎛ + ⎝ ⎞ ⎠ − = ⎛ ⎝ ⎞ ⎠ ⎛ + ⎝ ⎞ ⎠ − ≈ ≈ ⋅ ⋅ We often round to the nearest cent, or in this case, to $387.48. However, because $387.48 is slightly less than the answer we obtained, we will round our answer up to $387.49 to ensure that the Burnettes reach their goal of $55,000. 7 TECHNOLOGY TIP Scientific Calculator To determine the sinking fund payment in Example 2, we evaluated the expression ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎛ ⎝⎜ ⎞ ⎠⎟ − 55,000 0.033 12 1 0.033 12 1 (12.10) This expression can be evaluated on a scientific calculator, as follows: y 55000 ( 0.033 12 ) ( (1 0.033 12) ( 12 10 ) 1 ) x × ÷ ÷ + ÷ × − After the = key is pressed, the answer 387.48442 is displayed. ( Continued) Amriphoto/E+/Getty Images
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