B = Starting Portfolio
P = Annual Investment (at the end of each year ... increasing with inflation)
R = Annual Return on Investments
I = Annual Rate of Inflation
x = 1 + R
y = 1 + I
z = x/y
then your Portfolio, after N years and N investments, is:

(1)   BxN + Py(xN - yN)/(x - y)     or     BxN + PyN+1 (zN - 1)/(z - 1)

• If you start investing IMMEDIATELY (instead of waiting till the end of the first year), then just replace P by P/y in the above formulas.
• If you WITHDRAW P at the BEGINNING of each year (like, when you retire ... and this withdrawal increases with inflation), and you start with a Portfolio worth $B, then the balance in your Portfolio (after N years and N withdrawals) is obtained by replacing P by P/y (so the withdrawals start IMMEDIATELY ) and P by -P (that means your investment is really a WITHDRAWAL). You then get the formula:

(2)   BxN - P(xN - yN)/(x - y)     or     BxN - PyN (zN - 1)/(z - 1)

• If you want to know how long your Portfolio will last, set the above Portfolio balance, (2), to zero and determine the number of years, N, like so:

(3)   N = -log(1 - (B/P)(z - 1)) / log(z)

where log is a logarithm (to any convenient base).

What about TAXES?

• If you're building your Portfolio within a Registered Retirement Savings Plan (RRSP), you get a tax break ... you get a tax refund for the money you invested.
• If your tax rate is T (for a 43% tax rate, you put T = .43), you get a tax refund of QT for an investment of Q so it only costs you P = Q - QT = Q(1 - T). Hence, if you put up $P, your annual investment is $Q = P/(1-T).
  
• To see the effect on your Portfolio, just replace P by P/(1 - T), in the formula (1), above (where now P refers to how much of your money you invest, each year).

• If your Portfolio is outside an RRSP you pay taxes on the gains (when you sell something and actually do make a gain ... that is, you crystalize your gains).
  Suppose the tax rate on these gains is t (which depends upon the type of gain: interest, dividends or capital gains).
  Then, when a Portfolio worth $A increases to A(1+R), a crystalized gain of AR gets reduced, via taxes, by an amount tAR, so you're left with a gain of AR(1-t). It's like getting a Return of only R(1-t).
  To see the effect on your Portfolio, just replace R by R(1 - t) in the formula (1), above.

and Mortgages?

If you get a $B mortgage, then, after N months, the balance owing is given by formula (1), with inflation I = 0 (since your monthly payments don't change with inflation), so y = 1 + I = 1 and we get a balance of

(4)   BxN - P(xN -1)/(x - 1)

after N months and N monthly payments.

Of course, x = 1 + R, as usual, but now R is the monthly interest rate!
It's given by the magic formula R = (1 + Q/2)^1/6 - 1 where Q is the annual mortgage rate.

If, after N months, your balance is zero (for example, after 240 months meaning 20 years), then
Bx^N - P(x^N -1)/(x - 1) = 0
so we can find the monthly payments:

(5)   P = BR/ (1 - (1 + R)-N)

where we have put x = 1 + R ... cuz that's what x is!

and Annuities?

You can use magic formula (5) to determine what the annual payments would be if you put up $B to get an N-year annuity (with annual interest R). If you give yourself an annuity from your investment portfolio then use R = your annual Rate of Return. If you buy an annuity from company ABC, then use R = their interest rate (which is likely to be about half of your Rate of Return).

In formula (5), you can also do it monthly: let N = number of months and R = monthly Rate which is calculated differently than for mortgages. If Q is the annual Rate, then the monthly Rate is:

(6)   R = (1 + Q)1/12 - 1

and now you take money OUT of your portfolio ...

If the withdrawal, say $P, is from an RRSP, then all of P is taxable. That's the easy situation.