\(A=P\left(1+\dfrac rn\right)^{nt}\)
\(\dfrac AP=\left(1+\dfrac rn\right)^{nt}\)
\(\ln\dfrac AP=nt\ln\left(1+\dfrac rn\right)\)
\(\dfrac{\ln\frac AP}{nt}=\ln\left(1+\dfrac rn\right)\)
\(e^{\ln(A/P)/(nt)}=1+\dfrac rn\)
\(e^{\ln(A/P)/(nt)}-1=\dfrac rn\)
\(n\left(e^{\ln(A/P)/(nt)}-1\right)=r\)
