Solving compound interest formula for n

Question

Given A=P(1+(r/n))^nt, how can you solve for n?

Answer 1

Divide both sides of the equation by P: A/P = (1 + (r/n))^nt.

Take the natural logarithm (ln) of both sides of the equation: ln(A/P) = ln((1 + (r/n))^nt).

Apply the power rule of logarithms, which allows you to bring the exponent down as a coefficient: ln(A/P) = nt * ln(1 + (r/n)).

Divide both sides of the equation by t * ln(1 + (r/n)): ln(A/P) / (t * ln(1 + (r/n))) = n.

Simplify the right side of the equation: n = ln(A/P) / (t * ln(1 + (r/n))).