Question

On 2/7/2019, the Powerball was listed at $224 million. The “cash value” was listed as $136.4 million (this is the lump-sum immediate payment option). If you choose the annuity option, you’ll receive the $224 million in 30 equal installments, with the first payment immediately. If your interest rate is 5%, which option should you choose? What if it’s 3%?

Answer 1

interest rate at 5%

PV of annuity option

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 7.46666666666667*((1-(1+ 5/100)^-30)/(5/100))*(1+5/100)

PV = 120.52

choose lumpsum option as it has higher value of 136.4 mln

interest rate at 3%

PVAnnuity Due = c*((1-(1+ i)^(-n))/i)*(1 + i )

C = Cash flow per period

i = interest rate

n = number of payments

PV= 7.46666666666667*((1-(1+ 3/100)^-30)/(3/100))*(1+3/100)

PV = 150.74

this time choose annuity option as it has higher PV than lumpsum option