Magic Penny Parable

Question

Suppose you discover a magical U.S. nickel (5 cent piece) that has the power to double (in quantity) each day when placed in fertile soil. After being planted in the soil for one day you now have 2 nickels, after two days you have 4 nickels, after three days you have 8 nickels, and so on. What is the dollar value of the nickels after 25 days?

Answer 1

on day 25, you have 5 + 10 + 20 + 40 + 80 + ... 

 

This is a geometric sequence with a₁= 5, r = 2, and n = 25.  Therefore, the Sum = (25(1-2²⁵))/(1-2).

 

this will equal 25(1-33554432)/(-1) = $83,886,077.

 

No, invest this at 4% for 5 years and you will be rich.