The other thing that can make a big difference is the yearly income tax we pay. And when we pay it. For example if inflation is 3% pa and you have money sitting in a bank account that earns 3% pa, you can still be getting behind unless you can find some cost effective way to delay paying the tax on the income earned.

And another real killer is if an item you are interested in buying is highly sought after for any reason and price pressures are forcing it to go up by considerably more than the after tax rate of return you can get on your savings/investments, then you are still getting behind on your purchasing power re that item.

It's for reasons like those that people with some cash will often eventually decide that having cash in the bank earning interest isn't a great investment and look for other things to invest in. Things that will give them a higher after tax rate of return than cash in the bank. And a higher after tax rate of return than inflation generally. Or even a higher after tax rate of return than the rate of increase in price on some specific asset type they want to purchase. But with higher returns come higher risks; By and large.

Year Price Increase
0 $100.00 $-
1 $103.00 $3.00
2 $106.09 $3.09
3 $109.27 $3.18
4 $112.55 $3.28
5 $115.93 $3.38
6 $119.41 $3.48
7 $122.99 $3.58
8 $126.68 $3.69
9 $130.48 $3.80
10 $134.39 $3.91

So if you have $100 today you can buy the basket of groceries. But in 10 years time you'll need $134.39 to buy that same basket of groceries. But if you've put the $100 you have today "under the matress" as they say, in 10 years time it will still be $100. So it isn't going to buy you that $134.39 basket of groceries.

If inflation is running higher, the calcs get nastier way more quickly. As in at 10% pa inflation, in 10 years time you'd need $259.37 to buy what $100 would buy you today.

Sean, your calc is wrong because you are working off the flawed assumption that inflation of 3% pa reduces the purchasing power of your money by 3% pa. It doesn't. Rather, it increases the price of something by 3% pa. I don't know what a graphing calculator is or how to use one, but I suspect the fact you are putting in a calc that involves -.03 is the cause of the problem. Inflation makes the price of something go up. It's an increase. Namely a positive amount.

Tim, you're closer to the mark. In that you accept you've got the same amount of money as you started with. But you are making a mistake when you say "Prices can keep going up at 3% of your dollar (3 cents) every year" - Working off the $100 figure I used above, prices go up by 3% of the original $100 in the first year (namely by $3) and that makes the item's price $103. So in the second year it goes up by 3% of that new increased price. Namely 3% of $103. Which is an increase of $3.09. And so on with the effect continuing to be cumulative.

Percentage increases and decreases can be confusing. You have to remember what base figure you are working from. And that every time you get a percentage increase or decrease, the base figure will be different for the next calc.

An example - Some people might feel quite happy if they'd heard that the stock market went down by 50% then went up by 50% - It could seem quite natural to assume they had got back any loss they'd made. But if a person starts off with a base amount of $100 and that goes down by 50% they will have lost $50. So they'll have $50 left. And that $50 they have left is the new base number for the next percentage increase or decrease calculation. So when someone says the market has now gone up by 50%, it is 50% of that new base figure of $50 that the market has gone up by. Namely its gone up by $25. So they now have the $50 it went down to, plus the $25 it has increased by. Namely $75. Which is a fair bit short of their original $100.

And from a practical point of view, don't swallow any figure of 3% pa inflation (or 4%) or whatever "they" are quoting. That might be the case if you are up to your ears in debt, have to use lots of petrol and go on holidays regularly. But if not, if could well be 10% pa or even higher right now for you. It just depends what you spend your money on/save for.

Also inflation is a pretty abstract thing. Just because there might be inflation in an economy does not mean it affects your world as much as the quoted inflation figures. For example inflation in late 2007/early 2008 in Australia was getting a kick up because of high oil prices, but if you walked to work and did not own a car then the impact on your economic life would be less than a someone driving a V8 sports car to the office everyday

To tie this in with the article above, your mathematical formula which essentially describes exponential decay or growth (albeit towards a non-zero equilibrium point), doesn't help individuals protect their wealth - it serves the issuers of money only, as they use such devices to whittle away people's savings.

To put it simply, what used to happen is the bully on the beach controlled the sand castle industry by lending out sand at interest, so that everybody's sand castle got smaller unless they went to borrow more. It could have gone on forever, actually. But what is now happening is that the bully on the beach is (arbitrarily) going to knock over your sand castle, take his sand back and get you to build his sand castle for him - and then make you promise to suck up to him forever or else he won't let you play on the beach any more. That's my take on the economy.