How do I extract j from, B = A.(1 + j)^N + (P/j).[(1 + j)^N - 1]?
with an initial Amount deposited, then regular (usually) monthly Payments (deposits).
The standard way to show is: F = A(1 + i)^n + (P / i)[(1 + i)^n - 1] , where:
F = Future value, A = initial Amount deposited, P = regular Payment,
n = Number of regular payments, i = periodic Interest rate.
As example, $1000 deposited initially, then $100 per month for 36 months at annual
rate of 6% compounded monthly ( i becomes .06/12 = .005):
F = 1000(1.005)^36 + (100 / .005)(1.005^36 - 1) = 5130.29102....
It is not possible to solve for i directly; must be done numerically.
If you google "iteration", you'll get an idea of what's involved.
It really becomes "guessing", then "homing in" until you hit paydirt!