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Question 75593: Her parents have given Silly Sally a choice of payment method for her allowance: She can receive $25.00 dollars at the end of two weeks or she can get $.01 today and double that, $.02 tomorrow and double that for each day doubling the amount from the day before every day for two weeks. Decide which type of payment Sally should pick by calculating the amount she receives for each.
Found 2 solutions by Edwin McCravy, Earlsdon:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
Her parents have given Silly Sally a
choice of payment method for her
allowance: She can receive $25.00
dollars at the end of two weeks or
she can get $.01 today and double that,
$.02 tomorrow and double that for each
day doubling the amount from the day
before every day for two weeks. Decide
which type of payment Sally should pick
by calculating the amount she receives
for each.
The second choice for payment is the
sum of a geometric series Sn,
a1(rn - 1)
Sn = 覧覧覧覧覧覧
r - 1
where n = 14 days, a1 = 1st term = .01,
r = common ratio (multiplier) = 2
.01(214 - 1)
S14 = 覧覧覧覧覧覧覧
2 - 1
.01(16384 - 1)
S14 = 覧覧覧覧覧覧覧覧
1
S14 = .01(16383) = $163.83
Certainly this better than $25.00
Edwin
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! Well, Silly Sally ought to ask her math teacher for help on this before she decides.
If she accepts the $25.00-offer, she will, of course, have $25.00 at the end of the two-week period.
If, however, after consulting with her math teacher, she decides to accept the second offer, she would soon see that this is the better offer because, after 14 days, she would get a total of pennies. This equals $163.83:
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