Solving for n in Present Value and Annuity formula

Question

I derived the formula for n=.... of the following formula P = $\ 525 $

A = $\ 15 $

i = $\ 0.015 $

Answer: $\ 50 $

P = $\ A [\frac{((1+i)^n - 1) }{ (i*(1+i)^n)}]$

n = $\ \frac{ln(\frac{Pi}{A})} { ln(\frac{i}{(1+i)})} $

I know this is correct. However, I don't get the answer of n when I plug-in all the values for P,i,and A. Why? n= is not incorrect, is it?

Answer 1

If you manipulate the expression you get

$$P = A\dfrac{\left[(1+i)^n - 1\right]}{i(1+i)^n}$$

$$(1+i)^n(\frac{Pi}{A}) = (1+i)^n-1$$

$$(1+i)^n \left[1-\frac{Pi}{A}\right] = 1$$

$$(1+i)^n = \dfrac{1}{\left[1-\frac{Pi}{A}\right]}$$

Taing log on both sides

We get

$$n log(1+i) = log\left(\dfrac{1}{\left[1-\frac{Pi}{A}\right]}\right)$$

$$n = \dfrac{log\left(\dfrac{1}{\left[1-\frac{Pi}{A}\right]}\right)}{log(1+i)}$$

$n = \dfrac{log\left(\dfrac{1}{(1-\frac{Pi}{A})}\right)}{log(1+i)}$

If you substitute the value you get n = 50