If the nominal interest rate is equal to 5%, and the inflation rate is equal to -5%, then what is the real interest rate?Single choice
A
None of the other answers.
B
9.673%
C
10.526%
D
10%
E
0%

Question

If the nominal interest rate is equal to 5%, and the inflation rate is equal to -5%, then what is the real interest rate?

BlackTom AI · Accepted Answer

First, we restate what is given and what is being asked: a nominal interest rate of 5% and an inflation rate of -5% (deflation), and we need the real interest rate.
Option A: None of the other answers. This would be true only if none of the listed values match the real rate. Since at least one option matches the correct calculation, this option is not correct.
Option B: 9.673%. This value does not align with the standard formulas for converting nominal rate and inflation into a real rate. It seems to be a numerical artifact that does not correspond to either the approximate or the exact Fisher calculation in this scenario.
Option C: 10.526%. This is the exact real interest rate when you use the Fisher equation, which states (1 + nominal) / (1 + inflation) − 1. Substituting nominal = 0.05 and inflation = −0.05 gives (1.05) / (0.95) − 1 ≈ 1.105263 − 1 = 0.105263, i.e., about 10.5263%. This option accurately reflects the compounding effect of deflation on the real rate.
Option D: 10%. This value corresponds to the commonly used approximate formula real ≈ nominal − inflation. Here, that approximation yields 5% − (−5%) = 10%, which is close but not exact; it ignores the compounding effect captured by the Fisher exact formula, so it is not the precise real rate.
Option E: 0%. This would imply no real return, which is inconsistent with having a positive nominal rate and negative inflation; it contradicts both the exact and approximate calculations in this scenario.
In summary, the significantly precise real rate computed via the Fisher equation is approximately 10.526%, which corresponds to Option C, while the other options reflect either an approximate result, a misapplication, or an incorrect interpretation of the relationship between nominal rate and inflation.

If the nominal interest rate is equal to 5%, and the inflation rate is equal to -5%, then what is the real interest rate?Single choice

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