P = A(1 + ni)
Which is close, but not exactly what you got. I could not find a single equation that had (1 + i)^n.
So we plug the values above into the equation above:
$20,000 = $10,000 (1 + .15n)
$20,000 = $10,000 + $1500n
$10,000 = $1500n
6.667 years = n
So that's how long it will take $10,000 to grow to $20,000.