Math Problem Statement

If the nominal one-year interest rate is 9.47% and expected inflation is 6.93% then what is the expected increase in purchasing power from saving for one year?

Solution

To determine the expected increase in purchasing power, we can use the Fisher equation, which relates nominal interest rates, real interest rates, and inflation:

1+r=1+i1+π1 + r = \frac{1 + i}{1 + \pi}

Where:

  • rr is the real interest rate (the expected increase in purchasing power),
  • ii is the nominal interest rate (9.47% or 0.0947),
  • π\pi is the expected inflation rate (6.93% or 0.0693).

We can solve for the real interest rate rr:

r=1+i1+π1r = \frac{1 + i}{1 + \pi} - 1

Substituting the values:

r=1+0.09471+0.06931r = \frac{1 + 0.0947}{1 + 0.0693} - 1

r=1.09471.06931r = \frac{1.0947}{1.0693} - 1

r0.0238 or 2.38%r \approx 0.0238 \text{ or } 2.38\%

So, the expected increase in purchasing power from saving for one year is approximately 2.38%.

Would you like more details or have any questions?

Here are 5 related questions:

  1. How does the real interest rate affect long-term savings?
  2. What happens if inflation exceeds the nominal interest rate?
  3. How would deflation affect the Fisher equation?
  4. What assumptions are made when using the Fisher equation?
  5. How can changes in inflation expectations impact investment decisions?

Tip: A positive real interest rate indicates that your purchasing power increases, meaning your savings will grow in value relative to inflation.

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Math Problem Analysis

Mathematical Concepts

Interest Rates
Inflation
Real Interest Rate

Formulas

Fisher equation: 1 + r = (1 + i) / (1 + π)
Real interest rate formula: r = (1 + i) / (1 + π) - 1

Theorems

Fisher Equation

Suitable Grade Level

College-level Economics or Finance