I don’t get this Tax Calculation For the situation where one is taxed at the realization of a capital gain FVIF=(1+r)^n(1-t)+t Why do we add the “t” back at the end?
it is a derivation… Look at it this way. you started out with 1$ it earned r% per year. At the end of n year 1$ had become (1+r)^n Now your capital gains = [(1+r)^n - 1] which is taxed at t. So your entire portfolio return = (1+r)^n - [(1+r)^n - 1]*t simplifying and keeping like terms together: it becomes: (1+r)^n(1-t) + t
Because capital gain tax is applied to the return and not to the principal, so the formula add back the amount of tax on the principal.
I like to memorize these formulas. Reminds me of plug and chug l2