## Office Hours: Costs of Inflation

Inflation can throw a kink in your savings plans. To accurately know your rate of return, you need to do a little more than calculate what you’ll receive off of the nominal interest rate.

First off, returns on savings are taxed. Depending on where you live in the world, you’ll need to take out some portion of your returns to pay taxes. For our example, we’ll use 33%.

If your nominal interest rate is 6% and you save $100, your return is $6 at the end of the year. Now we need to take out that third for taxes, which leaves you with $4.

So far, so good. But we still haven’t arrived at the real interest rate after taxes, which is the nominal interest rate minus inflation. If inflation has been at a fairly low 3%, that means that the real interest rate before taxes in this scenario is 3%.

To account for inflation, that’s another $3 out of your original $6 return.

We’re down to a $1 return off of your $100 investment, bringing your nominal interest rate of 6% to a real interest rate of 1%. Yikes! But it’s still a net positive.

What if the nominal interest rate is 12% and inflation is at a moderate 9%? You would actually lose money with real interest rate of -1%. Your $100 would be, at the end of the year, equivalent to $99 in real terms.

As inflation gets higher, you can expect your real interest rate to dip further into the negatives. It makes less sense to save money under high inflation. The rational action under this scenario is to go ahead and spend money as quickly as you get it. Sadly, this makes the problem even worse as an increased velocity of money also increases inflation.

For refreshers on how inflation works and the quantity theory of money, check out these videos:

- Zimbabwe and Hyperinflation: Who Wants to Be a Trillionaire?
- Measuring Inflation
- Quantity Theory of Money
- Causes of Inflation
- Costs of Inflation: Price Confusion and Money Illusion
- Costs of Inflation: Financial Intermediation Failure
- Why Governments Create Inflation

Are you struggling with a different practice problem or concept from an MRU video? Let us know! Head on over to our feedback forums to suggest a topic for a future Office Hours video.

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## Transcript

Today's practice question is about expected inflation, taxes, and saving. We know that the government taxes any nominal interest you earn on a savings account. So, for this scenario, let's assume a realistic 33% tax rate. Now, if you're rational, you should care mostly about your real interest rate after taxes when deciding how much to save. So, in each case, we'll calculate the nominal rate of return after taxes. And then, most importantly, that real rate of return after taxes, which takes inflation into account. As always, check out our video on inflation before trying to solve this problem.

And one final note, before we get started. Recall that the real interest rate is simply the nominal interest rate minus inflation. In each of these cases, the nominal interest rate has actually adjusted for inflation, such that the real interest rate before taxes is 3%. In other words, inflation is expected. No surprises here. The real interest rate after taxes, though, which we'll calculate, differs from case to case.

So, let's tackle that first case. Your savings account offers a nominal interest rate of 6%, and inflation is 3% that year, fairly low. To make this more concrete, let's assume you saved $100. So, at the end of the year, you earned 6% on your $100, or $6 in interest. The government will take a third of your $6 in taxes, so you'll get to keep 2/3. of $6, or $4. You started with $100 and earned $4 after taxes, so your nominal rate of return is 4%.

Now, to calculate your real rate of return after taxes, the rate that actually matters, we have to adjust for inflation. Inflation is 3%. So, after a year, your initial $100 would be equivalent to $103. So, you gain $4 after taxes from interest, but three of those dollars are just making you break even, given inflation. So, your real gain after taxes is just $1. Given that you saved $100, we could also view this as a real return of 1% after taxes.

Just to recap, before taxes and inflation, you earned 6%. But after taxes and inflation, your real gain was 1%. It's a lot lower, but it is still positive. How about that next scenario, when inflation is 9% that year and the nominal interest rate on your savings account is 12%. We won't convert our calculation to dollars this time. So, to calculate the nominal rate of return after taxes, we'll multiply the nominal interest rate, 12%, by what proportion we'll actually get to keep after taxes, 2/3, which equals 8%. Now, for the real rate of return, the one that matters, accounting for inflation as well: 8% minus inflation, which is 9%, equals -1%, a negative rate of return. Surprisingly, you lose money by saving when there are moderate levels of expected inflation.

Now, it's time to get more extreme. Let's say inflation is 87% per year, and the nominal interest rate is 90%. Once again, the nominal rate of return after taxes is 90 times 2/3, or 60%. And the real rate of return after taxes? 60% minus inflation, which is 87%, equals -27%. Would you invest in a company that Offered you a -27% rate of return? No! So why would you put your money in a savings account with similar results? And keep in mind, just sticking your money under your mattress is even worse, because then you wouldn't be earning any interest.

So, you would lose even more in real terms. Honestly, I'm scared to do that last calculation, so I'll leave it as a practice question after this video. Just think about how you would respond in this situation. If inflation were, say, 900% per year, the money supply is increasing such that prices are rising daily, and even though it's expected high inflation, the tax system discourages savings. The rational person in this instance would try to spend any money she got as fast as she could. And sadly, this actually makes the problem worse. Because if everyone does this, money is turning over more quickly, so velocity has also increased. The quantity theory of money predicts that prices will rise even more.

So, the surprising takeaway here is that even moderate levels of expected inflation, like our example of 9% inflation, can still lead to financial intermediation failure when the tax system distorts the real rate of return on savings.

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