How to find interest rates in compound interest formulas

If 6000 dollars invested in a bank account for 10 years, compounded quarterly, amounts to 8170.78 dollars, what is the interest rate paid by the account?

10 yrs = 40 quarters

A = P(1 + r)^n

8170.78 = 6000(1 + r)^40

(1 + r)^40 = 1.3618 (solve by logs or with scientific or financial calculator)

1 + r = 1.00775

r = 0.0775/quarter = 0.031 = 3.1%/yr

P=6000
A=8170.78
n=10*4=40 (compnd qwtrly)
R=r/4
A=P(1+R/100)^n
8170.78=6000(1+r/400)^40
8170.78/6000=((400+r)/400)^40
1.361793=((400+r)/400)^40
(1.361793)^1/40=(400+r)/400
1.0096967=(400+r)/400
r=1.0096967*400-400
r=3.8786799
r=3.9% approximately.

A = P * (1 + i/n)^(n * t)

A = 8170.78
P = 6000
n = 4
t = 10

8170.78 = 6000 * (1 + i/4)^(4 * 10)
8170.78 / 6000 = (1 + i/4)^40
(8170.78 / 6000)^(1/40) = 1 + i/4
i/4 = -1 + (8170.78 / 6000)^(1/40)
i = -4 + 4 * (8170.78 / 6000)^(1/40)
i = 0.03099999856067840801408110442198
i = 3.1%