How long (in years and months) will it take for an investment to double at 15% compounded quarterly?

First thing the formula is slightly mistated.

it should be

A=P (1+r/n) nt (you had rt fo the exponent and it should be nt

now lets solve this thing

you want A = 2P (double your money

2P = P (1+r/n) nt

we can divide through by P adn put in the values we know

2 = (1+.085/2) 2t

2 = (1.0425) 2t

and now we can take the log of both sides to make it easy to solve our equation

log (2) = 2tlog (1.0425)

.301 = 2t (.018)

divide both sides by. 018

16.653 = 2t

t = 8.327 (number of years to double your money at this rate

check it

(1.0425) 16.653 = 2