I have this formula for amortization
PMT = PV * (i / (1 - (1+ i)^(-n) ) )
I'm having issues isolating n in cases where I'm given the present value, the payment value, and the interest rate, but not n.
Let's say I have:
PV = $800 i = 0.015 PMT = 51.04
I'm trying to solve for n as follows:
51.04 = 800 * (0.015 / (1 - (1.015)^(-n) ) )
0.0638 = 0.015 / (1 - (1.015)^(-n) )
ln(0.0638) = ln(0.015) - ln(1 - (1.015)^(-n) )
ln(0.0638) - ln(0.015) = - ln(1 - (1.015)^(-n) )
I have no idea what to do with ln(1 - (1.015)^(-n) ) to be quite frank, or if I'm even on the right track with that, I feel I'm missing something basic. However, in this case, I know n is equal to 18, but I have 0 idea how to get to that.
You have $$PMT=\frac {iPV}{1-(1+i)^{-n}}\\ 1-(1+i)^{-n}=\frac {iPV}{PMT}\\ 1-\frac {iPV}{PMT}=(1+i)^{-n}\\ \log\left(1-\frac {iPV}{PMT}\right)=-n\log(1+i)\\ -\frac{\log\left(1-\frac {iPV}{PMT}\right)}{\log(1+i)}=n$$