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In December 2012, a retired waitress in Massachusetts won a lottery of $5.6 million.  They can either...

In December 2012, a retired waitress in Massachusetts won a lottery of $5.6 million.  They can either give her a lump sum of $5.6 million or pay her $320,000 immediately and then $320,000 per year for the next 19 years. The time value of money to her is 8 percent. What choice will she make and why? (Ignore the tax effect).

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Answer #1
Lottery amount lump sum given today = 5600000
Present value is 5600000
or
Annuity at beginning = 320000
No. of annuities = 20
Interest rate = 8%
Present value of annuity due formula = Annuity + Annuity * (1- (1/(1+r)^(n-1)))/r

320000 + (320000*(1 - (1/(1+8%))^(20-1))/8%
3393151.744

Present value of $320000 received now and in next 19 years have present value of only $3,393,151.74

So, He will choose lumpsum lotterly amount of $5600,000 as present value in this case is more.

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