Inflation and Real Returns — Practice Quiz

A Financial Math cheat sheet for Inflation and Real Returns — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. If the real interest rate $r$ is $3\%$ and the inflation rate $\pi$ is $2\%$, what is the approximate nominal interest rate $i$?

   • $1\%$
   • $5\%$
   • $6\%$
   • $0.06\%$

   Answer: $5\%$

2. A nominal interest rate $i$ of $7\%$ is observed during a period of $4\%$ inflation $\pi$. What is the approximate real interest rate $r$?

   • $3\%$
   • $11\%$
   • $28\%$
   • $0.03\%$

   Answer: $3\%$

3. Calculate the exact nominal interest rate $i$ if the real interest rate $r$ is $4\%$ and the inflation rate $\pi$ is $3\%$. Round your answer to two decimal places.

   • $7.00\%$
   • $7.12\%$
   • $12.00\%$
   • $1.07\%$

   Answer: $7.12\%$

4. If the nominal interest rate $i$ is $6\%$ and the inflation rate $\pi$ is $2\%$, what is the exact real interest rate $r$? Round your answer to two decimal places.

   • $4.00\%$
   • $3.92\%$
   • $8.00\%$
   • $1.04\%$

   Answer: $3.92\%$

5. For a real interest rate $r$ of $5\%$ and an inflation rate $\pi$ of $5\%$, how much does the approximate nominal interest rate $i \approx r + \pi$ differ from the exact nominal interest rate $1 + i = (1 + r)(1 + \pi)$?

   • $0\%$
   • $0.25\%$
   • $0.50\%$
   • $1.00\%$

   Answer: $0.25\%$

6. Under which condition is the approximate Fisher equation $i \approx r + \pi$ generally considered most accurate?

   • When inflation rates are very high.
   • When real interest rates are very high.
   • When both inflation rates and real interest rates are low.
   • When nominal interest rates are negative.

   Answer: When both inflation rates and real interest rates are low.

7. An investment yielded a nominal return $i$ of $8\%$. If the real return $r$ was $5\%$, what was the exact inflation rate $\pi$ during this period? Round your answer to two decimal places.

   • $3.00\%$
   • $2.86\%$
   • $13.00\%$
   • $1.03\%$

   Answer: $2.86\%$

8. If the nominal interest rate $i$ is $10\%$ and the real interest rate $r$ is $6\%$, what is the approximate inflation rate $\pi$?

   • $4\%$
   • $16\%$
   • $60\%$
   • $0.04\%$

   Answer: $4\%$

9. A financial analyst is forecasting interest rates for a period of expected high inflation ($15\%$) and a target real return of $3\%$. Which formula should be used to calculate the nominal rate for the most accurate prediction?

   • The approximate Fisher equation $i \approx r + \pi$.
   • The exact Fisher equation $1 + i = (1 + r)(1 + \pi)$.
   • Simple addition of real rate and inflation rate without considering compounding.
   • The formula for continuous compounding.

   Answer: The exact Fisher equation $1 + i = (1 + r)(1 + \pi)$.

10. According to the exact Fisher equation $1 + i = (1 + r)(1 + \pi)$, if the inflation rate $\pi$ is positive, how does the nominal interest rate $i$ compare to the real interest rate $r$?

    • $i$ is always less than $r$.
    • $i$ is always equal to $r$.
    • $i$ is always greater than $r$.
    • $i$ can be greater than or less than $r$ depending on the value of $r$.

    Answer: $i$ is always greater than $r$.