Compound Interest.

FV = PV (1+i)^n

1 = 1x10^-6 (1+i)^1000

1/1x10^-6 = (1+i)^1000

10^6 = (1+i)^1000                  take log of both sides

6 = 1000 log(1+i)

6/1000 = log (1+i)       raise 10 to both sides

 

 10^(6/1000) = 1+i

i=1.3911%

Here is another way!

 

1 =1/1,000,000 x (1 +i)^1,000      divide both sides by 1/1,000,000

1,000,000 = (1 +i)^1,000               take 1/1,000th root of both sides

1,000,000^(1/1,000) = 1 + i

1.013911385........     = 1 + i           subtract 1 from both sides and multiply by 100

i =1.3911385%.