Question

You expect inflation over the next year to be 4.6%. Actual inflation over the last year was 0.78%, and the current nominal interest rate is 0.51%. What is your expected real rate of interest (in %)? Round to 0.01%. E.g., if your answer is 3.145%, record it as 3.15.

Answer 1

Using the Fisher formula, Real Interest Rate can approximately be calculated as Nominal Interest rate minus Inflation rate.

Nominal Interest rate = Real interest rate + Inflation Rate

=>Real Interest rate = Nominal Rate - Inflation Rate

So, Expected Real Interest Rate (Approx.) = 0.51% - 4.6% = -4.09% (approx.)

This is just approximate rate, as it is mathematically incorrect to add percentage rates like this.

Mathematically, percents should be multiplied for addition, and divided for subtraction.

So, the correct mathematical formula for Fisher effect is,

(1 + Nominal Interest Rate) = ( 1 + Real Interest rate) (1 + Inflation Rate)

Given that, Nominal Interest Rate =n = 0.51%

Expected Real Interest Rate = r

Expected Inflation Rate next year = i = 4.6%

So, (1+n) = (1+r)(1+i)

=> (1+r) = (1+n) / (1+i) = (1 + 0.51%) / (1 + 4.6%) = 1.0051 / 1.0460 = 0.96089866156

=> 1 + r = 0.96089866156

=> r = 0.96089866156 - 1

=> r = - 0.03910133844 = -3.91 %

Therefore, Expected Real Interest Rate is -3.91% (minus 3.91%)