A lottery winner must decide between two methods of payment. Choice one is to receive a lump sum of $100,000,000. Choice two is to begin with one cent on day 1, three cents on day 2, nine cents on day three, and so on until the end of 22 days.

Part 1: Which choice should the lottery winner select? (4 points)

Part 2: Using complete sentences, explain the procedure taken to answer this question. (4 points)

Question

A lottery winner must decide between two methods of payment. Choice one is to receive a lump sum of $100,000,000. Choice two is to begin with one cent on day 1, three cents on day 2, nine cents on day three, and so on until the end of 22 days. 

Part 1: Which choice should the lottery winner select? (4 points) 

Part 2: Using complete sentences, explain the procedure taken to answer this question. (4 points)

tpaulus · Answer

The second is better, because it increases exponentially

campbell_st · Answer

the 2nd method is a geometric sequence with the 1st term a = 0.01  and the common ratio is 3

so you could calculate the number of days to reach $10 000 000 using the formula

$$10 000 000 = 0.01 \times 3^{n -1}$$

guess and check on a calculator by changing the value of n would allow to to calculate the time needed to surpass the lump sum 

but method 2 has a downfall... passing away early would mean option 1 was the better choice.

anonymous · Answer

By showing you the general method for calculating choice #2, we'll do both together.

3^0  +  3^1  +  3^2  +  . . .  +  3^21

(3^22   -   1)/(3 - 1) = 15690529804 cents   =  $156905298.04

amistre64 · Answer

the choice of "better" depends on other factors not account for

mathstudent55 · Answer

Why guess? Use 22 days and see if it's more money than choice 1.

campbell_st · Answer

well as I said, you can find when option 2 surpasses option 1... 

providing you don't pass away early...

mathstudent55 · Answer

If you're concerned whether you're going to survive the next 22 days, then you're in bad shape.

campbell_st · Answer

lol... well it is an option to do with choices.... that a lot of people don't consider when looking at questions of this type...and as an 8th grader... it was my 1st thought

anonymous · Answer

im Here:)

anonymous · Answer

so we have to solve 
3^0  +  3^1  +  3^2  +  . . .  +  3^21

(3^22   -   1)/(3 - 1) = 15690529804 cents   =  $156905298.04

tcarroll010

anonymous · Answer

It's already solved.  Just look to the right of the "=".

anonymous · Answer

ohh wow lol thanks. 
Do you mind helping me with one more?

mathstudent55 · Answer

@campbell_st 
One more remark. Your equation takes into account only the amount one would receive on a certain day, but the 22-payment method is a total of 22 payments, so it's a cummulative amount.

campbell_st · Answer

no just use the formula for a sum of a geometric series

$$S_{22} = \frac{0.01 ( 1 - 3^{22})}{1 - 3}$$

that will give the total amount provided after 22 days...

campbell_st · Answer

@mathstudent..why pick on an 8th grader