find the total accumulated value (in dollars) of this income stream at the end of 3 years. (Round your answer to the nearest dollar.)

Question

Future Value of an Investment

 An investment is projected to generate a continuous revenue stream at the rate of

R(t) = 30,000e^0.02t

dollars/year for the next 3 years. If the income stream is invested in a bank that pays interest at the rate of 5.5%/yearcompounded continuously, 

Answer 1

FV = e^0.0·55·3∫₀³30000e^0.02t·e^{- 055t}dt = 30000e^0.165∫₀³e^{- 0.035t}dt = 30000e^0.165e^{- 0.035t}/(- 0.035)₀³ =

30000e^0.165(e^{- 0.105} - 1)/(- 0.035) = $100762.78