Question

7. 0/2 points v || Previous Answers ly Notes Ask Your Teacher V For the past 15 years, an employee of a large corporation has been investing in an employee sponsored educational savings plan. The employee has invested $8,000 dollars per year. Treat the investment as a continuous stream with interest paid at a rate of 4.5% compounded continuously. (a) How much money is in the savings account today? (Round your answer to the nearest cent.) $ 171383.6 x (b) How much money would have had to be invested 15 years ago and compounded at 4.5% compounded continuously to grow to the amount found in part (a)? (Round your answer to the nearest cent.) $ 87261 Submit Answer

Answer 1

(a) The formula for calculating future value of a continuous stream investment, compounded continuously is, FV = f pe174\dt Where FV is future value, P is continuous stream investment for I years and r is the rate compounded continuously. The objective is to find present value of provided investment. First find the future value of the provided continuously stream investment, FV = Pe(74\dt sof0e949-lat = 8000e10129 2043 dt 15 15712.2638-e0,045376 = 0.045 Jo Further simplify the above equation: 15712.2638 0.0454 715 2045 Led =171368

The future value after 15 year is $171368. Now, formula of present value is, PV = FV PT Substitute future value , r and T in the formula, PV - 171368 (0.045-15) = 87253.33 Therefore, present value is $87253.33). (b) The objective is to find the investment done 15 year ago to grow the amount found in part (a). Consider the formula, PV = FY 87253.33 0.045.15 = $44425.59

Thus, the investment of $44425.59 should be made 15 years ago to grow the amount found in above part.