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# Prizewinner in a sweepstakes.

Discussion in 'Economics' started by GFX007, Jun 21, 2009.

1. ### GFX007

Greetings to all members.

I'm trying to solve this problem:

==========================

James is a major prizewinner in a sweepstakes. He has the option of either receiving a single check
for \$125,000 now or receiving a check for \$50,000 each year for three years. (James would be given
the first \$50,000 check now). At what interest rate would James have to invest his winnings for him
to be indifferent as to how he receives his winnings?

a) 15.5%
b) 20.0%
c) 21.6%
d) 23.3%
==========================

But I don't understand what does this mean:

"At what interest rate would James have to invest his winnings for him
to be indifferent as to how he receives his winnings?"

Should I find at what interest rate the sweepstakes invest the money?
P = A (P/A, i%, n)

2. ### maxitronixy

I would say b) 20%

To be "indiffrent" to his winnings, imo is how he would invest the smaller sum , 125 000 now to achieve "no difference" to his total payout of 150 000 over three years.

hence 150 000- 125 000= 25000

250 000/ 125 000 *100 = 0.2 or 20%

He would have to get an intrest rate of 20% of his 125 000 in total, as there are no other answers in this mcq, i assume it's the total accumalative rate over his princepal

all the other answers would lead to much more than 150 000 or less, hence , B)

3. ### peilthetraveler

Thats a strange question. When someone says what interest rate would he have to invest in, it usually implies yearly and not over 3 years. The question should've stated what Rate of Return would he have to get, not what interest rate should he get. The actual answer is "none of the above"

The interest rate to be indifferent is 6.266% The rate of return to be indifferent is 20%

4. ### maxitronixy

yeah it just the termiology in the questions used is wrong, it not uncommon for minor misprinting or wrongly phrased questions in mcqs , but if you have to put the answer in an exam question just chose b , unless there is an option to put none of the above, as most of my mcqs in uni are computer marked, with just 4 options

5. ### GFX007

............ nvmd

thanks for the help. !

6. ### maxitronixy

if it's just this four options, the termology is wrong, simple intrest is 6.266% per year or 20% accumalated

Simple intrest, 6.266% for three years, accumalted intrest 20% also called the rate of return,it means the same thing.

compound intrest A = P(1 + r)^n
p= 125 000, r is what u want to find, A is 150 000 N is 3 years

150 000=125 000(1+r)^3

r =0.0626585692 or 6.26% compounded annually

I really think your making this a lot more complicated than it actually is, and also u need to consider that the question is not specific amibigous

and you need to get \$25 000 ( returns) from \$125 000(amount invested). in three years

7. ### trendy

OK, you have two \$50,000 payments over two years. The question is what interest rate is needed on those two payments over the two years to equal the PV (present value) of \$75,000. Why \$75,000? Because that's the difference between the \$125,000 now payment, and the first \$50,000 payment which is also paid immediately. The answer is 21.525% Rounded to 21.6%

To verify, take \$125,000 and calculate the FV (future value) in two years using 21.6% interest. (\$184,832)

Then, calculate FV of \$50,000 for two years using 21.6, then add FV of \$50,000 @21.6 interest for one year, then add \$50,000. (\$184,832)

8. ### TGregg

I see a yearly interest rate of ~19.5% doing the trick. Most posters haven't thought this through very well. Are you sure the first answer is 15.5 and not 19.5?

Although the yield on that rate is ~21.5%. . .

EDIT I guess Trendy thought about it enough.

9. ### GFX007

Hi,

What did you do to solve it?

10. ### trendy

See my edited response above.

#10     Jun 21, 2009
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