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## Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,750 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the , since that choice has the greater present value. At an interest rate of 10% per year, the winner would be better off accepting , since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend? The lump sum is always better. The payments over time are always better. It will depend on the interest rate; advise her to get a calculator. None of these answers is good advice.

### Answers

PAYMENTS OVER TIME

To know the better option we would have to compute the Present Value of the Payments overtime payouts. That way we can equate it to the lump sum today.

To calculate the Present Value we will discount at the interest /discount rate of 6% except for the payment today which should not be discounted as this is the present.

= 1000 + 1000/(1+0.06) + 1000 / (1+0.06)^2

= 1000 + 943.396226415 + 889.996440014

The PV of the Payments overtime Option is higher than the lump sum payment today therefore winner would be better off accepting the PAYMENTS OVER TIME.

If you need any clarification do react or comment.

1) the payment over time ( $2833.39 )

2) the payment over time ( $2759.11 )

We get the lump sum today of $2750 which is exactly the value of this amount today and there is no need to discount this amount. We will compare this amount with the present value of the cash flows we will receive over time. If the present value of over time cash flows is more than lump sum payment, we will choose over time cash flows and vice versa.

1) The present at 6% for over time cash flows is,

PV = 1000 + 1000/1.06 + 1000/1.06^2 = $2833.392As 2833.392 is more than 2750, we will choose payment over time.

2) The present at 9% for over time cash flows is,

PV = 1000 + 1000/1.09 + 1000/1.09^2 = $2759.11As 2759.11 is more than 2750, we will choose payment over time.

✅✅✅ Correct answers: 1 🔴 question: Which lottery payout scheme is better? Suppose you win a small lottery and have the choice of two ways to be paid: You can accept the money in a lump sum or in a series of payments over time. If you pick the lump sum, you get $2,750 today. If you pick payments over time, you get three payments: $1,000 today, $1,000 1 year from today, and $1,000 2 years from today. At an interest rate of 6% per year, the winner would be better off accepting the , since that choice has the greater present value. At an interest rate of 10% per year, the winner would be better off accepting , since it has the greater present value. Years after you win the lottery, a friend in another country calls to ask your advice. By wild coincidence, she has just won another lottery with the same payout schemes. She must make a quick decision about whether to collect her money under the lump sum or the payments over time. What is the best advice to give your friend? The lump sum is always better. The payments over time are always better. It will depend on the interest rate; advise her to get a calculator. None of these answers is good advice.