Math Problem Statement

Suppose the real rate is 3.75 percent and the inflation rate is 1.5 percent. What rate would you expect to see on a Treasury bill?

Solution

To find the nominal interest rate (the rate expected on a Treasury bill), you can use the Fisher equation:

(1+i)=(1+r)(1+π)(1 + i) = (1 + r)(1 + \pi)

Where:

  • ii is the nominal interest rate (the rate you expect to see on the Treasury bill),
  • rr is the real interest rate (3.75% or 0.0375),
  • π\pi is the inflation rate (1.5% or 0.015).

Let's calculate ii:

1+i=(1+0.0375)(1+0.015)1 + i = (1 + 0.0375)(1 + 0.015)

1+i=(1.0375)(1.015)=1.053061 + i = (1.0375)(1.015) = 1.05306

i=1.053061=0.05306i = 1.05306 - 1 = 0.05306

Converting this to a percentage:

i=5.31%i = 5.31\%

So, the nominal interest rate you would expect to see on the Treasury bill is 5.31%.

Would you like further details or have any questions?


Here are some related questions:

  1. How does the Fisher equation relate real and nominal interest rates?
  2. How would the Treasury bill rate change if inflation were higher?
  3. What assumptions does the Fisher equation rely on?
  4. Can nominal interest rates be negative?
  5. How do inflation expectations impact bond prices?

Tip: Always adjust for inflation when comparing returns over time, as real interest rates account for the eroding effect of inflation on purchasing power.

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Math Problem Analysis

Mathematical Concepts

Interest Rates
Fisher Equation
Inflation Adjustment

Formulas

(1 + i) = (1 + r)(1 + π)

Theorems

Fisher Equation

Suitable Grade Level

Grades 11-12 or College Level