Can someone please show me how this is rearranged/simplified from this: PV = CF[(1-(1+r)^-n)/r] to PV= CF(1/r)[1-(1/((1+r)^n)] with steps, will help me wrap my head around it.
Also, how does it go from the Sum of c/(1+r)^n to those formulas in the first place?
Note: PV is the present value, CF is cash flow, r is rate, and n is periods (for context).
I would appreciate any help! I can't find anything specific to the rearrangement for this online, and not sure what to search for...
So, let's start with the first initial formula,
PV = CF [ (1 - ((1+r)^-n)) / r ]
We can first expand the numerator as such,
PV = CF [ (1/r) - (((1+r)^-n) * (1/r)) ]
Then factoring out (1/r),
PV = CF (1/r) [ 1 - ((1+r)^-n) ]
PV = CF (1/r) [ 1 - (1/((1+r)^-n)) ]