In today's world, saving for retirement can be very challenging. That's because the cost of living has gotten so exorbitant. High inflation over the past five years has led to a surge in the prices of food and housing, as well as just about everything else, while wages seem to rise at a much slower pace. The idea of saving $1 million for retirement can seem like a daunting prospect.

However, it's completely doable, even for someone on a modest income. The key lies in patience and compounding returns.

Time, time, time

Not only is saving difficult, but investing is as well. Sure, you'll hear about people who invested in a meme stock or cryptocurrency and got rich overnight, but those stories are far and few between. Then, of course, there are billionaires like Warren Buffett, who have consistently outperformed the benchmark S&P 500 index for six decades and make it look easy.

However, even Buffett will acknowledge that one of the reasons his returns have been so good is that he has been investing for so long. And that's really the key. Picking a stock that is going to double in one or two years is difficult, but picking one that will generate strong long-term returns over two or three decades is less difficult. In fact, historical data suggests the longer one holds stocks, the less likely they are to lose money.

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The lesson from all of this is that the earlier one starts investing and the longer one can hold stocks, the easier it is to accumulate significant wealth on a modest income.

Now let's take a look at some numbers. Let's say a person starts with $1,000 invested in their retirement account. In a traditional individual retirement account (IRA), individuals under the age of 50 can contribute up to $7,000 and in most cases deduct these contributions from their taxable income. The goal should therefore be to contribute as much tax-deductible money as possible to a retirement account each year.

Now, not everyone has that much to set aside, but let's say you could stash away $300 every month for your retirement for a total annual contribution of $3,600. Let's also say that you can expect to earn a 10% annual return on your money, which is the average annual return of the S&P 500 over the last 100 years.

While the S&P 500 is currently dominated by a few handfuls of high-flying artificial intelligence stocks, the market has also put up incredibly strong returns in recent years and is well on its way to delivering a third consecutive year of 20% gains or higher. A 10% long-term rate of return is still realistic.

If you were to save $3,600 annually for a decade with 10% annual returns, the $1,000 initial investment would turn into about $62,600, with 41% of the total value coming from compounded returns. If you were to do this for 20 years, the initial $1,000 would grow to over $222,000 with 67% of the total coming from your returns. And if you were to follow this investment strategy for 35 years, that $1,000 would grow into $1.05 million with 89% coming from the gains on your investments.

Consider how much the savings grow between years 20 and 35. That's because as your principal grows, the same 10% return is adding much more to your account balance. It's important, however, to understand that investment returns are not guaranteed, nor do they tend to trend upward in a straight line. There will be (stressful) years when your investment portfolio loses value. With a long enough time horizon, the volatility smooths out, and history has shown a 10% return is achievable.

Get rich slowly

In the end, what makes investing so difficult is the temptation to try to get rich quickly by investing in stocks that can multiply five or 10 times in just a few years. Americans see the immense wealth of a small minority on social media, in the news, and sometimes in their everyday lives, and it tempts them to take bigger risks to try to reach the end goal quickly.

However, meme stocks and meme tokens, as well as microcap stocks with quick multibagger potential, are extremely risky.

That's not to say you can't allocate some capital to strategic bets on growth or artificial intelligence stocks. But understand that the method above is tried and true and far less risky. Additionally, due to inflation, $1 million will most likely be worth significantly less in 35 years than it is now, so you need to factor that into your goals to maintain your purchasing power.