deferred capital gains and tax deferred

sorry i have a simple question, about deferred capital gains and tax deferred differences.

deferred capital gains formula:

FVIF = (1+r)^n * (1-T) + T

and tax deferred formula:

FVIF = (1+r)^n * (1-T)

Both are deferred taxes, why deferred capital gain has the extra T in the formula?

That term is returning the untaxed cost basis. Don’t want to pay taxes twice!

So for tax deferred, is tax deferred inclusive of deferred capital gain, deferred dividends, deferred incomes ? Why it does not add back the UNTAXED cost?

Because contributions to TDA are usually made on pre-tax basis and all withdrawals will be taxed at the moment of withdrawal.

In your first formula it is supposed that part of initial investment is not taxed in full thus part of tax on initial amount is added back.

It is missing a cost base, B at the end of formula which might not be 1.

Thus should be:

FVAT = Initial investment [(1+r)^N (1-T) + (T * B)]

Thank you very much. Got it.

You’re welcome.

BTW, I made an error in formula, should be + T*B at the end. Now, I have corrected it.

Tax deferred

Pre-tax AV: (1+r)^n

Taxable portion: (1+r)^n - 1

Tax payable: T *[(1+r)^n - 1]

After-tax AV = (1+r)^n - T * [(1+r)^n - 1] = [(1+r)^n - T * (1+r)^n] + T = [(1+r)^n] * (1 -T) + T