Imagine the amount of money you spend per year is X, and you are currently earning (after taxes) twice that, 2X. So you spend half your income, and save the other half. Even if those savings didn't yield any interest, you'd have 25X in savings after 25 years. With 4% interest yield you'd reach 25X in 18 years, thanks to the power of compound interest. If you have 25X money in the bank, you could stop working, and as long as you continue to get 4% interest, that would give you X per year, and you could live at your usual standard of living forever.

Calculations like the above paragraph are the basics of the FIRE (financial independence, retire early) movement. However, a savings rate of 50% is nearly impossible to achieve for most people. As long as you want to be at leased basically housed, eat regular meals that don't make you sick, and wear clothes good enough to go to work with, there is something like a minimum standard of living depending on local conditions; and not everybody earns twice that minimum. Due to that minimum, it is much easier for high income individuals to have a higher saving rate than for low income individuals.

But much of the difficulty of achieving a high savings rate is psychological. 36% of Americans who earn over $200,000 a year say they live paycheck to paycheck. As there are obviously other Americans with annual incomes of half that living in the same area, it is proven that these people could live on half their income; but they either have an inflated idea of how their living standard should look like, or they are trying to "keep up with the Joneses", and spend due to social pressure.

If you have a savings rate of zero, retirement will come as a shock. Wherever you live, old age pensions tend to be only a fraction of your last salary. On average in Europe pension levels are less than half of final salaries, but there is a distribution to that: If you already live of welfare, your retirement welfare check won't be much different from your current income. If you have an income from work, you have to pay a percentage of that into the pension system, and get a return based on what you paid in. The more you earn, the more you pay in, and the more you get out, but it doesn't scale perfectly. Various caps and rules result in the pension as a percentage of your final salary getting lower and lower, the higher your salary is. For example in the USA your pension benefits calculate as 90% of your monthly earnings below $1,226, 32% of your earnings between $1,226 and $7,391, and just 15% of your earnings above $7,391. If you do the numbers for an American with an annual salary of $200,000, he'll end up with social security benefits of only a quarter of salary. That'll be rough, if he previously thought he couldn't even live on half his salary.

For most people, neither the FIRE idea nor zero savings are financially viable. The good news is that with a moderate savings rate plus the state pension you'll be able to hold you standard of living. For example if you save 15% of your annual income every year for 40 years, and then retire with a state pension of half your previous salary, the interest on your savings should be able to make up for the other half. The real live calculation is complicated, as your annual salary over 40 years is probably going up, stock market returns aren't constant, and life has its financial ups and downs that make a constant savings rate difficult. The other complicated factor is that you can withdraw more of your retirement savings every year than just its interest yield. If you knew how long you will live, you could get both the interest rate and withdraw an amount of the capital at the rate that the savings run out the day you die. Not knowing when that is, and possibly wanting to leave money to your children, complicates that.

The important idea is that you can't spend all of your annual income on your living expenses. You need to be at least a bit frugal during the working portion of your life. If you don't, the pension system will impose a much more drastic frugality on you after retirement. The higher your savings rate, the more comfortable your retirement will become, and at some savings rate even retiring before working 40+ years becomes financially viable.