the value of an investment doubles in 15 years. Work out the interest rate

The actual interest rate depends upon the number of times that the investment is compounded per year.

Assuming that it is compounded once per year, using the compound interest formula:

       A  =  P(1 + r)^t

with A = 2 (representing twice the initial value),     P = 1 (representing the initial value),     and t = 15:

      2  =  1(1 + r)^15

--->   2  =  (1 + r)^15

Taking the 15th root of both sides:

--->  2^(1/15)  =  1 + r

--->  1.04729  =  1 + r

--->  0.04729  =  r

If you have a problem in which the compounding is more than once per year, or is compounded continuously, repost...