A customer invests $64,000 in an account that compounds 2.2% interest daily. The customer wants to change the investment when the account reaches $69,503.74 Use a graphing calculator and the equation 69,503.74=64,000(1+(0.022)/(365))^365x , where x is the time in years it will take to reach this amount. Solve for x , and round to the nearest hundredth if necessary.
Divide both sides by 64,000, then take the natural logarithm: x = ln(69,503.74/64,000) ÷ [365 ln(1 + 0.022/365)]. This gives x ≈ 3.75 years, so the customer should change the investment after about 3.75 years. The correct choice is D, 3.75 years.
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