Question

Lucky Larry wins $6,000,000 in a state lottery. The standard way in which the state pays such lottery winnings is at a constant rate of $240,000 per year for 25 years. Round your answer to the nearest $10. If Lucky invests each payment from the state at 6% compounded continuously, what is the accumulated future value of the income stream? Preview What is the accumulated present value of the income stream at 6%, compounded continuously? (This amount represents what the state has to invest at the start of its lottery payments, assuming the 6% interest rate holds.) Preview Points possible: 10 License This is attemnt 1 of 5

Answer 1

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1. Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cummulative amount available in Future)

C= Periodic cash out flow. 240000

r =effective interest rate for the period. 6.1836% = 0.061836

n = number of periods. 25

FV= 240000× {[(1+0.061836)^n]-1}/0.061836

FV = $13,513,131.37 (Answer).

2. Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at Present)

C= Periodic cash flow.

r =effective interest rate for the period.

n = number of periods.

PV = 240000× [1-(1+0.061836)^-25]/0.061836

PV = $3,015,187.17 (Answer).