Suppose you win the lottery, and the jackpot is $50,000,000!
You may either choose the annual payment option or the lump sum cash option. If you choose the annual payment option, then you will receive 20 equal payments of $2,750,000 – one payment TODAY and one payment at the end of each of the next 19 years. If you choose the lump sum option, then you will receive $39,194,650.87 today. Suppose you can invest the proceeds at 3.25%.
Which option should you choose? Please round to 4 decimal places.
First option ; Annual payment
Annual payment each (P)= 2750000
Interest rate (I)= 3.25%
Number of payment (n)= 20
Payment start today, so it is Annuity due.
Present value of Annuity due formula = P+(P*(1-(1/(1+I)^(n-1)))/I
Second : lump sum
It has same present value as amount is Received today.
Present value = 39,194,650.87
We will choose option having highest present value.
As option 1, Annual payment of 2750000 option has highest present value. So we will choose option first
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