On March 6, 2007, the Associated Press reported that Ed Nabors had won half of a

Question

On March 6, 2007, the Associated Press reported that Ed Nabors had won half of a $390 million jackpot, the largest lottery prize in US History. Suppose he was given the choice of receiving his $195 million share paid out continuously over 20 years or one lump sum of $120 million paid immediately.

Which option is better if the interest rate is 6%, compounded continuously? an interest rate of 3%?

Sketch together nice graphs of    y=9.75((1-20 e^{r})/ r ) and y = 120; mark the intersection point and find its decimal approximation (at least 4 digits after the demical dot). Hint: Xmin=.001; Xmax=.1; Ymin=80; Ymax= 190.

If Mr. Nabors chose the lump sum option, what assumption was he making about interest rates?

I really need step by step help please.

Explanation / Answer

This will be based on the formula P=Poe^rt

P = Future value
Po = Present value
e = the dreaded e
r = interest rate
t = time (years)

at 6%, you would have 195,000,000 = Po*e^(0.06*20)
divide both sides by everything to the right of the Po and you have
195,000,000 / e^(1.2) = Po
58,732,871.32 = Po

at 3%, same thing 195,000,000 = Po*e^(0.03*20)
195,000,000 / e^(0.6) = Po
107,018,269 = Po

So we have present values of
Lump sum payout now (present value) of 120M
6% 20 year payments using a present value of 58M
3% 20 year payments using a present value of 107M

Obviously he assumes the lump sum payout is the most advantageous, with the 6% deal being the worst, based on the present values

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