Math Problem Statement

What would you expect the nominal rate of interest to be if the real rate is

3.73.7

percent and the expected inflation rate is

6.76.7

​percent?

Question content area bottom

Part 1

The nominal rate of interest would be

enter your response here​%.

​(Round to two decimal​ places.)

Solution

To calculate the nominal rate of interest, we use the Fisher Equation:

i=r+π+(rπ)i = r + \pi + (r \cdot \pi)

Where:

  • ii is the nominal interest rate,
  • rr is the real interest rate (expressed as a decimal),
  • π\pi is the expected inflation rate (expressed as a decimal).

Given:

  • r=3.73%r = 3.73\% or 0.03730.0373,
  • π=6.7%\pi = 6.7\% or 0.0670.067.

Calculation:

  1. Calculate the direct sum of the real rate and inflation rate: r+π=0.0373+0.067=0.1043r + \pi = 0.0373 + 0.067 = 0.1043

  2. Calculate the interaction term rπr \cdot \pi: rπ=0.03730.067=0.0024991r \cdot \pi = 0.0373 \cdot 0.067 = 0.0024991

  3. Add the components together to find ii: i=0.1043+0.0024991=0.1067991i = 0.1043 + 0.0024991 = 0.1067991

  4. Convert to a percentage and round to two decimal places: i=10.68%i = 10.68\%

Final Answer:

The nominal rate of interest would be 10.68%.

Would you like additional explanations or examples? Here are 5 related questions:

  1. How does the Fisher Equation account for inflation in interest rate calculations?
  2. If the inflation rate doubles, how would the nominal interest rate change?
  3. Why is the interaction term rπr \cdot \pi included in the calculation?
  4. How does a negative inflation rate (deflation) affect the nominal rate?
  5. What is the difference between real and nominal interest rates in practice?

Tip: Always express rates as decimals during calculations to avoid errors when using percentages!

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Math Problem Analysis

Mathematical Concepts

Interest Rates
Inflation Adjustment
Financial Mathematics

Formulas

Fisher Equation: i = r + π + (r × π)

Theorems

Fisher Effect Theorem

Suitable Grade Level

Undergraduate Level or Advanced High School (Grades 11-12)