Question

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.

Answer 1

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

=2750000 +(2750000*(1-(1/(1+3.25%)^(20-1))/3.25%)

=41282655.97

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