If your employer asked you to select one of these options: a) Your salary for the next two months will be $5,000, b) 1 penny for the first day and then he will double your salary every day for the entire month, which one should you pick? How much will you have at the end of 30 days?

Question

If your employer asked you to select one of these options:   a)  Your salary for the next two months will be $5,000,  b) 1 penny for the first day and then he will double your salary every day for the entire month, which one should you pick?  How much will you have at the end of 30 days?

anonymous · Answer

A penny or a dollar?

anonymous · Answer

a penny

anonymous · Answer

wow i wish i could get this job!

anonymous · Answer

i know right!!

anonymous · Answer

penny...right

anonymous · Answer

option b

anonymous · Answer

i knew it was option B but I wasn't sure how much it would be.  I detest logarithms!!

anonymous · Answer

or even the formula

anonymous · Answer

day one 1 cent
day two 2 cents
day three 4 cents 
day four 8 cents
day five 16 cents
haven't made much yet
day six 32 cents 
day seven 64 cents 
double each time

general idea is that at day $n$ you will make $2^{n-1}$ cents to try $2^{30}$ on your calculator (assuming the month has 31 days) and be amazed at how much money you will have

anonymous · Answer

$$a _{n}=a _{1}*r ^{n-1}$$

anonymous · Answer

where a1 = 0.01, r = 2, and n = 30

anonymous · Answer

looks like about $1073741824$ pennies or $\$10,737,418.24$

anonymous · Answer

in order to find the amount on the 30th day. not the sum.

anonymous · Answer

@satellite73 gave the grand total.

anonymous · Answer

true the total will be twice that much  minus one cent

anonymous · Answer

the amount you'd receive on day 30 alone is like $5M

anonymous · Answer

oh my mistake 
i didn't read the 30 days in the month part sorry

anonymous · Answer

thanks for your help...I wish ya'll were my tutors everyday...ughhh I have finals on Saturday

anonymous · Answer

should be $2^{39}$ for the 30th day for a total of $2^{30}-1$

anonymous · Answer

damn typo 
$2^{29}$ for the 30th day, $2^{30}-1$ in total

anonymous · Answer

No the power is subtracted by 1

anonymous · Answer

It's cool.

anonymous · Answer

what @coreylvaughn  said
i made a typo there

anonymous · Answer

39th power would be sweet too though @satellite73 ! : )

anonymous · Answer

so the final salary would be $10,737,418.24 times 2 -1?

anonymous · Answer

Just $10,737,418.23

anonymous · Answer

.23

anonymous · Answer

I'll type the equation for geometric series...

anonymous · Answer

okay i see that is the sum at the end of 30 days...
Im slow with algebra please forgive me

anonymous · Answer

$$S _{n}={a _{1}(1-r ^{n})\over(1-r)}$$

anonymous · Answer

$$S _{30}={0.01(1-2^{30})\over(1-2)}$$

anonymous · Answer

$$=$10,737,418.23$$

anonymous · Answer

thanks :)

anonymous · Answer

Anytime. Take care

anonymous · Answer

I would pick the penny option. In 30 days (about one month) you would make about $536,870,912! Wish I were paid like that.