Pv Annuity Formula

In the future value of an annuity formula:

PV * [(1 + r) fv ^ n - 1] / r =

how do I solve for r? Thank you.

Formula:
= SUM ([1 + r] ^ n)

Answer: SUM ([1 + r] ^ n)

Applying the formula above, assume $ 1,000 deposit per year for 3 years at 10% compounded annually:
$ 1,000 = (1.1 + [1.1 * 1.1] + [1.1 * 1.1 * 1.1])
$ 1,000 = (1.1 + 1.21 + 1.331)
= $ 1.000 (3.641)
= $ 3,641

Proof (sales per year, with a 10% interest):
1st year
+ 0.1 = $ 1,000 ($ 1,000)
= $ 1,000 + $ 100
= $ 1,100

2nd year
= $ 1,100 + $ 1,000 + 0.1 ($ 1,100 + $ 1,000)
+ 0.1 = $ 2,100 ($ 2,100)
= $ 2.100 + $ 210
= $ 2,310

3rd year
= $ 2,310 + $ 1,000 + 0.1 ($ 2,310 + $ 1,000)
+ 0.1 = $ 3,310 ($ 3,310)
= $ 3,310 + $ 331
= $ 3,641

complete the appropriate number of P, N, F, V and solve an equation as normal.