The Math Behind Whether Saving $20 a Week Is Worth It

One extremely contentious topic in personal finance is whether it’s worth it to worry over small amounts. For instance, is saving $20 a week worth it?

The conventional wisdom is that, because of the power of compound interest, small savings make a big difference in the long run. The new thinking is that you should focus on a few big wins and then switch to thinking about growing your income.

In the debate, you’ll often hear people talk about buying lattes. There’s nothing special about a latte, it’s just a stand-in for a trivial expense of $3 or so. The thinking is that many people buy a latte at Starbucks every day, how much could they save over the long term if they cut this small expense?

In this post we’re going to break down the math to see how much saving on a small expenses can actually be worth in the long-term. We’ll consider saving $20 a week, or a little less than $3 a day. How much money would these savings compound to by the time you retire? How much income would you earn off it going forward? We’ll also consider whether there are other options to explore besides cutting back on small purchases.

$20 a Week Compounded for 40 Years

Saving $20 a week works out to saving $1,040 a year. Let’s assume you start saving when your career starts and you have a normal career of about 40 years. We’ll also assume you get a 6% rate of return.

Here’s what the growth of your investment would look like:

Years	Amount Saved	Returns	Portfolio Value
40	$41,600	$129,010	$170,610

Through the magic of compound interest, you only invested $41,600, but you ended up with over $170,000—over four times the amount you put in.

So it’s not insignificant, but it’s also not enough by itself to retire on. It’s sort of in that weird middle area. For a lot of people, and extra $170,000 would be a huge boost to their chances of retiring comfortably. It’s clearly not nothing. But it’s also not the difference between poverty and riches.

It’s worth asking, how much is $170,000 worth in retirement?

The 4% Rule

It’s helpful to think of investing as consisting of two stages:

• The wealth accumulation phase when you are saving money and letting your investments grow
• The wealth preservation stage when you are living off your nest egg and trying to make it last.

The “trying to make it last” part is an inexact science. We don’t know how long you will live, and we don’t know what rate of return your investments will earn in the future.

One simple rule of thumb we can use is called the 4% rule. It says that you can withdraw 4% of your initial balance every year (adjusted upward for inflation) with minimal chance of your portfolio failing.

The 4% Rule: How Much Money Do You Need to Never Work Again?

So the $170,610 we have from investing $20 a week generates $6,824 a year ($131 a week) of passive income according to the 4% rule.

It will take you a little over six years of retirement before the income that you pull out of your portfolio exceeds the amount that you invested in to your portfolio. If you enjoy a 20 year retirement, that extra $170,610 will have produced a total of $136,488 in passive income. And the principal balance will still be left over. It may have even grown.

So after 20 years of retirement, our initial $170,610 is actually likely worth more than $300,000: The $136,488 in passive income earned over 20 years plus the portfolio balance which may have grown beyond the initial $170,610.

The Time Frame Matters

Of course, maybe you want to retire early. Or maybe you’re already 20 years into your career and you haven’t been cutting back on small expenses. Whatever the reason, if your time frame is shorter, the value of the savings will be as well.

Here’s what your savings look like if you are only able to save for 20 years:

Years	Amount Saved	Returns	Portfolio Value
20	$20,800	$19,752	$40,552

That $40,552 portfolio is worth about $1,622 a year ($31 a week) of passive income according to the 4% rule. It will take you a little more than 12 years of retirement to pull out as much as you put in.

The Rate of Return Matters

While a short time frame makes things look worse, a higher rate of return makes them look much better. I ran the numbers with a 6% rate of return, which is fairly conservative. The historical rate of return on stocks has been much higher.

Jack Bogle, the founder of Vanguard, inventor of the index fund, and author of The Little Book of Common Sense Investing argues that because of lower dividends, decreased prospects for earnings growth, and high market valuations, we should expect fantastic returns over the next several decades. I agree and think it’s prudent to plan conservatively, but maybe everyone is wrong and the market will go to the moon.

Let’s see what happens if we run the numbers using a rate of return that has been more typical for the stock market.

The Impact of a 9.5% Rate of Return

Since 1926 (the first year we have S&P 500 data), the stock market has returned about 9.5% per year. And that extra 3.5% makes a big difference in our analysis:

Years	Amount Saved	Returns	Portfolio Value
40	$41,600	$398,569	$440,169

Holy cow. You cut your spending by less than $3 a day and ended up with nearly half a million dollars.

That $440,169 portfolio is worth $17,607 a year ($339 a week) in passive income. It will take you just over two years to take out more than you put in.

The Impact of a 12% Rate of Return

Years	Amount Saved	Returns	Portfolio Value
40	$41,600	$851,908	$893,508

This is just ridiculous. Your $893,508 portfolio can theoretically spit out $35,740 a year ($687 a week) in passive income. It will take you just over a year to take out more than you put in.

Often the people who advocate for saving money on small daily purchases assume generous returns like 12%. You can see why. If we had assumed a savings of $5 a day instead of just under $3, this imaginary portfolio would be worth over $1.5 million. The higher the rate of return, the more small expenses hurt.

Cutting Small Expenses Isn’t the Only Way to Save $20 a Week

So the math that uses the best estimates comes out somewhere in the middle of the debate. The math that uses aggressive estimates favors the savers. But the argument that favors the spenders doesn’t rely on estimates.

Whatever rate of return you get, you don’t need to cut small purchases to find more money to invest. One approach is to focus on the “big wins” of frugality. Most people spend more on housing and transportation than any other category. Locking in savings in those areas can be more powerful than relying on willpower to cut daily spending.

For instance, finding an apartment that is $100 a month cheaper would save you more than cutting a $3 expense every day, and eventually you’d get used to where you live and it would require no ongoing effort.

Big Wins the Simple Way: The 80/20 Approach to Saving Money

You could also get money to invest by increasing your income. This could be through a raise, a promotion, or even a side hustle.

Making money is hardest in the beginning and gets easier over time. The nice thing is that we aren’t talking about huge sums here. We’re talking about replacing $20 a week of cutting costs with $20 a week of income. You don’t need the world’s most lucrative side hustle to make that a reality.

Of course, the benefit of a side hustle is that it can scale up much better than cutting costs. Cutting a $3 expense is much easier than making $3, but the more you repeat this game, the harder it is to save and the easier it is to earn.

Earning More The Simple Way

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The Psychology of Money

Money isn’t just about the numbers. We all need to figure out how to use the numbers to change our behavior without rubbing our human nature the wrong way.

Cutting that morning latte is going to be more difficult if it’s the one thing that you look forward to every morning as you go to a job that you hate.

Instead of trying to swim against the current, it’s worth thinking about how you can manipulate your environment to make saving money easier. One approach that I advocate is called the “quick wins” project. The idea is simple: take a few days to go over all your bills and find out how to lower them.

You can do this by cancelling the service, switching to a competitor, downgrading, or negotiating.

Here’s how to do it:

Quick Wins the Simple Way: The Fast Path to Frugality

Or maybe you find that cooking in bulk causes you to eat meals at home. Eating meals at home is a great way to save, because no matter how you run the numbers, cooking is cheaper than eating out.

The Math Behind Why Cooking is So Much Cheaper Than Eating Out

None of This Matters If You Don’t Invest

If you aren’t intentional about setting aside money to invest, do you know what will happen to the $3 you save on that latte? You’ll spend it on something else.

There’s nothing inherently wrong with spending. Ultimately the reason why you’re investing is to spend money in the future. The key is that if you don’t ever invest, you’ll have to earn every dollar that you ever spend. When you invest, your money makes money so that you don’t have to.

Investing The Simple Way

Final Thoughts

Yes, small expenses can make a big difference, but remember that there are other ways of tackling this problem. The most important thing is that you have an intentional plan for controlling your spending, increasing your earnings, and investing the difference.