Whats your real rate of return if your savings account pays 2.5% interest and inflation is at 1

16.14 The Fisher Equation: Nominal and Real Interest Rates

When you borrow or lend, you normally do so in dollar terms. If you take out a loan, the loan is denominated in dollars, and your promised payments are denominated in dollars. These dollar flows must be corrected for inflation to calculate the repayment in real terms. A similar point holds if you are a lender: you need to calculate the interest you earn on saving by correcting for inflation.

The Fisher equation provides the link between nominal and real interest rates. To convert from nominal interest rates to real interest rates, we use the following formula:

real interest rate ≈ nominal interest rate − inflation rate.

To find the real interest rate, we take the nominal interest rate and subtract the inflation rate. For example, if a loan has a 12 percent interest rate and the inflation rate is 8 percent, then the real return on that loan is 4 percent.

In calculating the real interest rate, we used the actual inflation rate. This is appropriate when you wish to understand the real interest rate actually paid under a loan contract. But at the time a loan agreement is made, the inflation rate that will occur in the future is not known with certainty. Instead, the borrower and lender use their expectations of future inflation to determine the interest rate on a loan. From that perspective, we use the following formula:

contracted nominal interest rate ≈ real interest rate + expected inflation rate.

We use the term contracted nominal interest rate to make clear that this is the rate set at the time of a loan agreement, not the realized real interest rate.

Key Insight

• To correct a nominal interest rate for inflation, subtract the inflation rate from the nominal interest rate.

More Formally

Imagine two individuals write a loan contract to borrow P dollars at a nominal interest rate of i. This means that next year the amount to be repaid will be P × (1 + i). This is a standard loan contract with a nominal interest rate of i.

Now imagine that the individuals decided to write a loan contract to guarantee a constant real return (in terms of goods not dollars) denoted r. So the contract provides P this year in return for being repaid (enough dollars to buy) (1 + r) units of real gross domestic product (real GDP) next year. To repay this loan, the borrower gives the lender enough money to buy (1 + r) units of real GDP for each unit of real GDP that is lent. So if the inflation rate is π, then the price level has risen to P × (1 + π), so the repayment in dollars for a loan of P dollars would be P(1 + r) × (1 + π).

Here (1 + π) is one plus the inflation rate. The inflation rate πt+1 is defined—as usual—as the percentage change in the price level from period t to period t + 1.

πt+1 = (Pt+1 − Pt)/Pt.

If a period is one year, then the price level next year is equal to the price this year multiplied by (1 + π):

Pt+1 = (1 + πt) × Pt.

The Fisher equation says that these two contracts should be equivalent:

(1 + i) = (1 + r) × (1 + π).

As an approximation, this equation implies

i ≈ r + π.

To see this, multiply out the right-hand side and subtract 1 from each side to obtain

i = r + π + rπ.

If r and π are small numbers, then rπ is a very small number and can safely be ignored. For example, if r = 0.02 and π = 0.03, then rπ = 0.0006, and our approximation is about 99 percent accurate.

The investing information provided on this page is for educational purposes only. NerdWallet does not offer advisory or brokerage services, nor does it recommend or advise investors to buy or sell particular stocks, securities or other investments.

Your savings account balances and investments can grow more quickly over time through the magic of compounding. Use the compound interest calculator above to see how big a difference it could make for you.

Using this compound interest calculator

• Try your calculations both with and without a monthly contribution — say, $50 to $200, depending on what you can afford.

• This savings calculator includes a sample rate of return. To see the interest you can expect, compare rates on NerdWallet.

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Here’s a deeper look at how compounding works:

What is compound interest?

For savers, the definition of compound interest is basic: It’s the interest you earn on both your original money and on the interest you keep accumulating. Compound interest allows your savings to grow faster over time.

In an account that pays compound interest, such as a standard savings account, the return gets added to the original principal at the end of every compounding period, typically daily or monthly. Each time interest is calculated and added to the account, the larger balance earns more interest, resulting in higher yields.

For example, if you put $10,000 into a savings account with a 0.50% annual yield, compounded daily, you’d earn $51 in interest the first and second years, and $53 the third year. After 10 years of compounding, you would have earned a total of $513 in interest.

But remember, that’s just an example. For longer-term savings, there are better places than savings accounts to store your money, including Roth or traditional IRAs and CDs.

Compounding investment returns

When you invest in the stock market, you don’t earn a set interest rate but rather a return based on the change in the value of your investment. When the value of your investment goes up, you earn a return.

If you leave your money and the returns you earn invested in the market, those returns are compounded over time in the same way that interest is compounded.

If you invested $10,000 in a mutual fund and the fund earned a 7% return for the year, you’d gain about $700, and your investment would be worth $10,700. If you got an average 7% return the following year, your investment would then be worth about $11,500.

Over the years, your investment can really grow: If you kept that money in a retirement account over 30 years and earned that average 7% return, for example, your $10,000 would grow to more than $76,000.

In reality, investment returns will vary year to year and even day to day. In the short term, riskier investments such as stocks or stock mutual funds may actually lose value. But over a long time horizon, history shows that a diversified growth portfolio can return an average of 6% to 7% annually. Investment returns are typically shown at an annual rate of return.

The average stock market return is historically 10% annually, though that rate is reduced by inflation. Investors can currently expect inflation to reduce purchasing power by 2% to 3% a year.

Compounding can help fulfill your long-term savings and investment goals, especially if you have time to let it work its magic over years or decades. You can earn far more than what you started with.

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Compounding with additional contributions

As impressive as compound interest might be, progress on savings goals also depends on making steady contributions.

Let’s go back to the savings account example above. We started with $10,000 and ended up with a little more than $500 in interest after 10 years in an account with a 0.50% annual yield. But by depositing an additional $100 each month into your savings account, you’d end up with $21,821 after 10 years, when compounded daily. The interest would be $821 on total deposits of $22,000.

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