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

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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?

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

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Similar Questions

Part 1Suppose you postpone consumption and invest at​ 6% when inflation is​ 2%. What is the approximate real rate of your reward for​ saving? Part 1 A. ​4% B. ​3% C. ​5% D. ​6%

Suppose you put $100 in the bank on January 1, 2017. If the annual nominal interest rate is 10 percent and the inflation rate is 5 percent, the real interest rate is ______ percent.

A year ago, you invested $10,000 in a savings account that pays an annual interest rate of 5%. What is your approximate annual real rate of return if the rate of inflation was 3.5% over the year?

You deposited your holiday bonus in your bank account on January 1, 2024. If the annual nominal interest rate is 4.3 percent and the inflation rate is 2.0 percent, you will earn ______ percent in real terms. Round your answer to the nearest tenth of a percent.

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