I can remember many, many years ago... I think it was 1st or second year algebra. It was a module on finite series. We went through all the time value of money derivations to the point we could derive them on our own (PV, Sinking fund, FV, annuity...). It was rigorous, but once you understood it, it was pretty trivial.

At the end of the module, our prof showed us how to derive the formula for an indexed annuity. That was pretty hairy, but the punchline he delivered went along these lines....*" All the math we have just slogged through is pretty much useless... none of these formulae relate to the real world. For instance... why should we derive a financial plan and assume that the interest rate is going to be constant? (as we get older, we grow more risk averse and our rate expectation goes down) or why should pmt levels stay constant? Might it not be better to design an annuity which has a higher pmt (adjusted for inflation) in the first 10 years to account for the fact that our lifestyle requirements may take a dip in our latter years? or surely these investment cash flows don't exist in a vacuum. You will need more income in the years prior to 60/65 before your CPP/OAS kick in, or before your loan is paid off... fixed payment (inflation adjusted) annuities don't allow for that. Or how about a planned-for sale of your cottage 10 years out?"*

The time value of money algebra is fine for teaching someone compound interest... the general implications of saving for retirement and subsequently living off the proceeds, but as practical, real life tools, they just don't cut it.

Now for the coupe de grace... Income Tax. The only element which has meaning (to me anyway) is the amount of cash (after tax) available to purchase beer, groceries and gas (as well as the occasional car every 5 years say)

The above-mentioned math will not solve that problem for the principal reason that the income tax formula is not linear... it is a complex calculation involving discrete tax brackets (indexed to inflation) age credits, loan interest deductibility, dividend tax credits.... it is a nightmare.

Why is it a nightmare, given that many of us still do our T1 by hand, you ask? Simple... the tax formula was designed to work from the top down, whereas for the purpose of financial planning, we need to start at the bottom (net income) and drive the T1 backwards. The simple question... *"how much should I draw from my RRSP such that I net (after tax) exactly $30,000?"*... sounds easy, but it isn't. Now throw in the reality that tax on our RRSP withdrawal doesn't live in a vacuum... we are taxed on investment growth on capital outside of our RRSP, maybe even at the dividend rate. We are receiving additional taxable income from CPP, a pension, an annuity. This is absolutely impossible to solve with even the most convoluted set of time-value-of-money formulae.

Thankfully, there is a way to solve these kinds of problems... recursion math. The way you would solve that simple 'how much to draw from my RRSP to return $30K after tax?' question can be done by hand. You simply continually shovel RRSP withdrawals into a T1 program until you get close to the answer. It can be time consuming... trial and erroring 10 , 20, 100 times until the exact $30K drops out, but it is do-able.

Before the modern day computer arrived, this would have been the way to solve the 'reverse tax' problem, but now, the computer allows us to solve the 'needs-based' (after tax driven) tax accurate financial planning problem quickly and easily. The bad news, is that spreadsheets are not sufficiently fast or flexible, however using a procedural language (C++, Basic, Fortran, ...) *will* solve the problem and allow it to converge in a reasonable (several seconds) period of time.

Sorry to ramble on like this, but is is kind of my life's (well the last 15 years anyway) work. I get sort of passionate about it.