# math urgent

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The state lottery (which has a 6% lottery tax) offers to pay winnings in 25 annual payments or one lump sum,
sometimes called a cash-out option. This week’s lottery has a jackpot of \$30 million and
a cash-out value of \$18.2 million. Granted that the odds are highly unlikely one would
win, which option should a winner take—annual payments or a lump sum? Why?
Show work and formulas used.
These are the formulas I am choosing between:
annuity: a1=(1-r^n)/(1-r) where a1 is the original amount (30M or 18.2M), r is the rate (.06), and n is the number of years (25).
or future value: FV=PV(1+i/n)^nt where PV is the present value (30M or 18.2M), i is the rate (.06), n is the number of compounds per year, and t is the time (25).

• math urgent -

I saw this question when you posted it yesterday. I did not answer it since it wasn't quite clearly stated. Is the 30 million split into 25 equal annual payments?? I will assume that.

In that case we are simply finding the present value of those payments

payment = 30 million/25 = 1200000
r = .06
n = 25
PV = 1200000( 1 - 1.06^-25)/.06
= \$15,340,027.37

So I would take the cash-out value of 18.2 million

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