**Math and personal finance** go hand-in-hand.

They match up well, like wine and cheese. Preferably low-cost wine and cheese, as would be more in line with responsible spending. We’re all about increasing net worth here 🙂

Anyway, back to money and math. Some of this is very straightforward. For example, the more money we have, the better! Pretty simple math there.

More involved but still simple concepts are those that involve computation. For example, the power of compounding is very clear. Also, concepts can be combined. A recent post on three important financial numbers highlighted this as well.

I was thinking of a few other ways that we can use math to think a little bit more about money, and to revisit some assumptions that we might have about it. Nothing complex, but just simple ways of looking at things that we can keep in mind to make sure we’re making the right moves. Here are 4 such examples:

**A Penny Saved is Not a Penny Earned**

Let’s say you got a bonus of $1,000 next week. Wouldn’t that be great! If you’re like me or similarly like-minded people, you might want to throw that straight into savings. The thing is, you can’t. Why?

We can’t forget about taxes, that’s why. Lets say you will end up paying 30% in taxes. In that case, the $1,000 earned resulted in $700 saved. Flipping it around, a penny saved required more than a penny to earn it.

That might not have been the exact meaning of the saying, but you get the idea: taxes take a bite out of what we can take home, much less save. Depending on the tax rates in different countries, it could be small amount or a much more significant factor.

**Losses Require Extra Work to Get Back to Even**

Take another example of $1,000. Just to make it easy, you know. This time, after-tax income. If you lose 20% of it, you’re down to $800. That’s no fun!

If you want to get that $200 back, you have to do better than gain 20% back. You have to grow that $800 by 25% in order to get back to $1,000. Losing money requires some work to recover, so be careful with certain risks!

**We Need to Do Better Than Save our Entire Raise**

It’s often mentioned in the personal finance blogosphere that a good way to save money is to set aside your annual raise. In other words, simply save your raise – on top of whatever else we’re saving.

I think we need to do better than that.

Here is what I’m thinking. Tacking on a few zeroes to that $1,000 example from the past two situations, let’s say a person makes a $100,000 salary. With an annual raise of 3%, that’s a nice $3,000 increase! The thing is, those taxes might take away a fair amount of it. For simplicity let’s say one-third of the increase disappears via tax, leaving us with $2,000 extra.

However, that remaining $102,000 won’t have the same purchasing power as it did the prior year. With 1% inflation, it would have about the same purchasing power as $101,000 did the prior year. Thus, our raise won’t get us too far ahead of where we were last year. Which is crazy, since raises aren’t guaranteed, and jobs aren’t a sure thing either.

**A Million Dollars Might Be Enough For Retirement, or It Might Be Way Too Little**

I picked a million dollars as just as a random number to use in this example, just to illustrate. Here’s what I’m thinking:

Let’s say a 50-year old person has $1 million, and wants to retire. If that person spends $5,000 per month on expenses, it means she has 200 months of living expenses that are covered. That’s over 16 years, and probably not enough.

If her twin sister has the same exact amount of money, but only spends $2,500 per month, that’s over 32 years of expenses covered. Clearly, a very different situation. An example of how spending habits and liabilities can impact one’s ability to retire, as well as an example of how thinking through the math can help us make better decisions on using financial resources.

*Do you think of money in these terms, with respect to the above 4 examples?*

Brian@ Debt Discipline says

I am starting to think about my money in these terms more and more each day. In your last example wouldn’t that 1 million dollar still be earning some type of interest over those 200 months, while drawing the $5k?

Squirrelers says

Great to think in these terms, it only helps. As for interest, yes interest would be earned when drawing the $5k – but over time it would be less than what would be earned in the other case in which the balance would last longer.

Moneycone says

The key is to think in terms of percentages instead of absolute values. As you rightly pointed out, a penny saved is a penny earned … and to add to that, a penny invested is a penny multiplied!

Squirrelers says

I’d actually say that in this case, a penny earned is more than a penny saved! Though to your point, a penny invested would multiply. Not to confuse things 🙂

Bryce @ Save and Conquer says

I also think of money in the mathematical sense that you discussed, although I obviously adjust it for our actual situation. As Brian pointed out, above, the million dollars would have some interest added to it. I would add that it should also have inflation subtracted from it each year. Pure interest payments typically do not stay ahead of inflation, so that’s why some amount of investment is usually necessary even after retirement.

Squirrelers says

Great that you’re thinking of such things. That’s the key point, we have to use our brain to figure things out for each of us based on our personal situation.

Marie at Family Money Values says

Math and money do go together! Math is fun, money is fun too. However, when it comes to saving, we always kept it simple and put aside what we could and what we had to. We also avoided raising our standard of living with any pay increases we got. Yes taxes do erode take home, and yes it is harder to make up for loses, but saving something for us was better than not saving.

Squirrelers says

Sounds great Marie!

Michael | The Student Loan Sherpa says

This is so true. A lot of times I will get emails with readers asking for advice. Time after time I come back to the same advice… do the math.

Bloggers tend to fall into the trap of making universal rules, but with most things finance, there is not one single answer. I think the best advice for people starts with discussing all the things that need to be considered and ends with doing the math.

Squirrelers says

I think you’re right on that sometimes there is a trap of coming up with universal rules. Some of them might apply to all of us, but many of them might really need to be customized in practice to fit our specific situation, goals, etc.

Paul @ The Frugal Toad says

If I only saved my raises I would be in big trouble come retirement! By saving 10-15% and at least 50% of all cash windfalls, including raises, one should be able to live a similar lifestyle in retirement. Thinking about finances in terms of mathematical and economic concepts such as time value of money and inflation are critical if consumers are to successfully manage their finances.

Barbara Friedberg says

Great examples. My favorite money – math examples involve compound returns. Time is the most valuable commodity when it comes to building wealth!