Question 75593
<pre><font size = 5><b>
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 S<sub>n</sub>,

      a<sub>1</sub>(r<sup>n</sup> - 1)      
S<sub>n</sub> = 覧覧覧覧覧覧
         r - 1

where n = 14 days, a<sub>1</sub> = 1st term = .01,
      r = common ratio (multiplier) = 2

       .01(2<sup>14</sup> - 1)      
S<sub>14</sub> = 覧覧覧覧覧覧覧
           2 - 1 

       .01(16384 - 1)      
S<sub>14</sub> = 覧覧覧覧覧覧覧覧
            1

S<sub>14</sub> = .01(16383) = $163.83

Certainly this better than $25.00

Edwin</pre>