You earned 26.3 percent on your investments for a time period when the risk-free rate was 3.8 percent and the inflation rate was 4.0 percent. What was your real rate of return for the period?

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Question restated: You earned 26.3 percent on your investments for a time period when the risk-free rate was 3.8 percent and the inflation rate was 4.0 percent. What was your real rate of return for the period?

Option 1: 21.67 percent. This value is close to the expected answer range, but it does not match the precise real rate calculated using the standard Fisher equation. To get the real rate, we should convert the nominal return into a growth factor and adjust for inflation rather than simply subtracting percentages. Specifically, real rate = (1 + nominal) / (1 + inflation) − 1. Substituting nominal 0.263 and inflation 0.04 gives (1.263 / 1.04) − 1 ≈ 0.214423..., or about 21.44%. The 21.67% figure would imply a slightly different method or rounding error that does not reflect the exact Fisher adjustment.

Option 2: 19.12 percent. This appears to reflect a straightforward subtraction of inflation from nominal return (0.263 − 0.04 = 0.223 or 22.3%), which is not how real returns are precisely computed when inflation affects the purchasing power of gains. It is also not aligned with the multiplicative Fisher approach that more accurately translates nominal returns into real terms.

Option 3: 20.12 percent. Like the previous option, this value seems to come from an approximate or incorrect adjustment rather than the precise formula. It may result from misapplying a linear approximation or misplacing decimal points, but it does not match the exact real return per the standard formula.

Option 4: 21.44 percent. Using the Fisher equation, real rate = (1 + 0.263) / (1 + 0.040) − 1 = 1.263 / 1.04 − 1 ≈ 1.214423... − 1 ≈ 0.214423..., which is about 21.44%. This method accurately accounts for the compounding effect of inflation on the nominal return and yields the precise real rate for the period.

Summary of reasoning across options: The key concept is that real return adjusts nominal returns for inflation using the multiplicative Fisher transformation, not a simple subtraction. The correct approach computes a growth factor for the investment, divides by the inflation growth factor, and subtracts 1. The resulting figure around 21.44% aligns with Option 4, while the other options arise from rounding, linear approximations, or misapplication of the adjustment.

FIN 220 01 Final Exam _ Fall 2025

You earned 26.3 percent on your investments for a time period when the risk-free rate was 3.8 percent and the inflation rate was 4.0 percent. What was your real rate of return for the period?

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