Suppose the nominal interest rate is 10 percent, the tax rate on interest income is 28 percent, and the inflation rate is 6 percent. Then the after-tax real interest rate is -3.2 percent.

Question

BlackTom AI · Accepted Answer

Interest income is taxed on the nominal return, so compute the after-tax real rate by first finding the after-tax nominal return and then deflating by inflation.

1) Relevant concepts
- Nominal interest rate (i) = 10% = 0.10.
- Inflation rate (π) = 6% = 0.06.
- Tax rate on interest income (t) = 28% = 0.28.
- Taxes are applied to the nominal interest earned, so after-tax nominal return = 1 + i*(1 − t).
- The exact after-tax real interest rate = (1 + after‑tax nominal)/(1 + π) − 1.

2) Step-by-step reasoning
Start with $1 of principal. Nominal interest earned = i = 0.10. Tax on that interest = t · i = 0.28 × 0.10 = 0.028. After-tax interest earned = i − t·i = i(1 − t) = 0.10 × 0.72 = 0.072. Final nominal amount = 1 + 0.072 = 1.072.

3) Intermediate calculations
- After-tax nominal return = 1.072.
- Real after-tax factor = 1.072 / (1 + π) = 1.072 / 1.06 ≈ 1.0113207547.
- After-tax real rate = 1.0113207547 − 1 ≈ 0.0113207547 = 1.1321% (approximately 1.13%).

4) Why the correct answer is correct
The exact computation yields about +1.13%, not −3.2%. The tax is applied to the nominal interest, and inflation erodes purchasing power; when both effects are combined the investor still obtains a small positive real return in this case.

5) Why the other option is incorrect
- "True" (that the after-tax real rate is −3.2%) is incorrect because no reasonable correct application of the tax-on-nominal formula produces a negative 3.2% result with these numbers. Common mistaken methods (e.g., subtracting tax rate directly or misapplying tax to the real rate) give different and incorrect values. The correct computations above produce ≈ +1.13%.

6) Conclusion
Therefore the statement is False. The correct after-tax real interest rate is about 1.13%, confirming the provided answer "False."

Suppose the nominal interest rate is 10 percent, the tax rate on interest income is 28 percent, and the inflation rate is 6 percent. Then the after-tax real interest rate is -3.2 percent.单项选择题

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