Real Interest Rate vs Nominal Interest Rate

The Fisher equation and the word hiding inside it

The AP formula is that the real interest rate equals the nominal interest rate minus the inflation rate. A loan at 6 percent in a year of 2 percent inflation earns a real return of 4 percent, while a loan at 3 percent in a year of 5 percent inflation earns negative 2 percent, meaning the repayment buys about 2 percent less than the sum lent would have bought at the start. The word doing quiet work is inflation, because it means two different things depending on when you ask. Before the loan is made only expected inflation is available, so the rate written into the contract embeds the lender's forecast and the resulting real rate is an expected one. After the fact, what matters is actual inflation, and the realized real rate is the nominal rate minus whatever inflation turned out to be. One caution: the subtraction is an approximation of the exact Fisher relationship, and it drifts once inflation is large. At a nominal rate of 50 percent and inflation of 40 percent the shortcut gives 10 percent while the exact calculation gives about 7.1 percent, though at the single-digit rates AP uses the approximation is fine. Practice at /calculate/real-interest-rate.

Which rate belongs on which graph

This is the distinction that costs the most points on free-response questions, and it is purely a matter of labeling. The money market plots the nominal interest rate on the vertical axis against the quantity of money on the horizontal axis, because holding cash means giving up the stated dollar return you could have earned elsewhere. The loanable funds market plots the real interest rate on the vertical axis against the quantity of loanable funds, because savers and borrowers are deciding about purchasing power over time rather than about dollar counts. The related point is that the Federal Reserve directly targets a nominal rate, the federal funds rate. It moves the real rate in the short run only because expected inflation adjusts slowly, so a cut in the nominal rate initially drags the real rate down with it. Once inflation expectations catch up, the real rate returns to where the supply of and demand for loanable funds put it, which is why the table says the real rate is roughly unchanged in the long run. More on the model is at /macro/loanable-funds.

Why unexpected inflation moves wealth between borrowers and lenders

Every fixed-rate loan is a bet on inflation, and the loser is whoever forecast it wrong. Take a loan written at a 5 percent nominal rate when both parties expect 2 percent inflation, so the expected real rate is 3 percent. If inflation instead comes in at 6 percent, the realized real rate is 5 minus 6, or negative 1 percent, and the borrower repays in money worth noticeably less than the money borrowed. Unexpectedly high inflation therefore transfers purchasing power from lenders to borrowers, and unexpectedly low inflation transfers it the other way. Two consequences follow that exams like to test. First, large fixed-rate borrowers, including a government whose debt is nominal and not inflation-indexed, gain from an inflation surprise. Second, because lenders know this, inflation that is anticipated gets priced in: they demand a higher nominal rate up front, which is the Fisher effect, so the redistribution comes only from the surprise and not from inflation everyone saw coming.

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