Question

You have just won a jackpot of $15,000,000 in the lottery and must choose between a lump sum

payment today of $10,000,000 or equal installments of $750,000 per year with the first

installment coming today and the remainder coming at the end of each of the next 19 years. If

you can invest the proceeds and earn 5 percent, which option should you choose? At what

interest rate would you be indifferent between the cash and annual payment options. You can

ignore the tax implications.

Answer 1

Case 1

Amount = 10000000$

monthly intrest = 5%

n = 12 compounded monthly

time period = 20years

Amount after twenty year = P ( 1 + r/n)^nt

Amount after twenty year = 10000000 ( 1+ [0.05/12])^12x5

Amount after twenty year = 12833586.79$

case2

Intial investment = 750000$

monthly intrest = 5%

n = 12 compounded monthly

time period = 1years

Amount after one year = P ( 1 + r/n)^nt

Amount after one year = 750000 ( 1+ [0.05/12])^12x1

Amount after one year = 788371.2$

Again 2nd year investment = 788371.2 + 750000 = 1538371.2$

monthly intrest = 5%

n = 12 compounded monthly

time period = 1years

Amount after 2 year = P ( 1 + r/n)^nt

Amount after 2 year = 1538371.2 ( 1+ [0.05/12])^12x1

Amount after 2 year = 1617077.19$

So the amount after 20years is = 26339458.86$

Thus case2 is the better choice of taking 750000$ per year fro next 20years