Suppose you win a small lottery and have the choice of two ways to be paid: You
ID: 2443131 • Letter: S
Question
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 $2,950 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.
FILL IN THE BLANK:
At an interest rate of 8% per year, the winner would be better off accepting the (lump sum/ payment over time) , since that choice has the greater present value.
At an interest rate of 10% per year, the winner would be better off accepting (lump sum/ payment over time) , 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.
Explanation / Answer
ANSWER:
1) When i = 8%
present worth of 3 equal payments = 1,000(p/a,i,n) + 1,000
pw of 3 equal payments = 1,000(p/a,8%,2) + 1,000
pw of 3 equal payments = 1,000 * 1.783 + 1,000 = $1,783 + $1,000 = $2,783
since lump sum payment of $2,950 is more then that of $2,783 , therefore we will choose lumpsum payment at 8%
2) When i = 10%
present worth of 3 equal payments = 1,000(p/a,i,n) + 1,000
pw of 3 equal payments = 1,000(p/a,10%,2) + 1,000
pw of 3 equal payments = 1,000 * 1.736 + 1,000 = $1,736 + $1,000 = $2,736
since lump sum payment of $2,950 is more then that of $2,736 , therefore we will choose lumpsum payment at 10%
3) The best advice would be option c as present value will depend upon interest rate and if the interest rate is less , the present value will be more and hence optionc that is It will depend on the interest rate; advise her to get a calculator.
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