Question

1. The Lottery Question

Congratulations: you have won the lottery and you have several decisions to make but you need information to make the correct decision.  The advertised value is a total value $500,000,000 payable equally over 20 years.  Lotteries that are paid over a fixed time period are generally contracted as an annuity purchased with an insurance company.

1. Another option for the payout is to take a lump sum payment.  If the lump sum payout is $220,526,250, what is the interest rate being used for the lottery?
2. Assuming you could invest the lump sum payout in the following manor:
   1. Year 1 thru 5 at 5%
   2. Year 6 thru 10 at 10%
   3. Year 11 thru 15 at 15%
   4. Year 16 thru 20 at 7%

Answer 1

Part A) If 500 million is to be distributed over 20 years in equal payment, so each payment will be 500/20 = 25 million

Now we need to calculate the rate of interest that will lead to a PV of 220,526,250

We are given the following information:

Annual payment	PMT	$      25,000,000.00
rate of interest	r	To be calculated
number of years	n	20
Annual Compounding	frequency	1
Future value	PV	$   220,526,250.00

We need to solve the following equation to arrive at the required r:

So the Required rate is 9.49%

Part B) At the given rate we can calculate the FV of 220,526,250 as follows: