How many days will it take you to gain $475 if your uncle will give you 1 cent and double the amount everyday?

Question

for instance you have 1 cent on day one, 2 cents on day two, 4 cents on day three, 8 cents on day four etc.

Answer 1

This is a geometric series. Learn the formula!

S_n = a(1 - rⁿ) / (1 - r)

47500 = 1(1 - 2ⁿ) / (1 - 2)

47500 = (1 - 2ⁿ) / -1

-47500 = 1 - 2ⁿ

-47600 = - 2ⁿ

47600 = 2ⁿ

 

2¹⁵ = 32,768

2¹⁶ = 65,536

 

So after the 16th day you have $475

Answer 2

$475 = 47500

 

This amount shall be met and greatly EXCEEDED in 16 days

Here's the numerical solution:

 

amount     total thus far

1
2                       3
4                       7
8                      15
16                     31
32                     63
64                    127 <--- 1 week
128                  255
256                  511
512                 1023
1024               2047
2048               4095
4096               8191
8192              16383 <--- 2 weeks
16384             32767 <--- 15 days
32768             65535

 

After 16 days, the total amount will be $655.35