Using the Fisher equation, calculate the nominal interest rate
𝑖
𝑡
(in percent).

Round your answer to the nearest tenth of a percent.

Question

Using the Fisher equation, calculate the nominal interest rate 
𝑖
𝑡
 (in percent).

Round your answer to the nearest tenth of a percent.

BlackTom AI · Accepted Answer

To apply the Fisher equation for nominal interest rates, we typically use the relationship i ≈ r + π^e, where i is the nominal interest rate, r is the real (ex-ante) rate, and π^e is the expected inflation rate. This approximation works well when the rates are not extremely large.

- Step 1: Identify the components. The Fisher framework separates the return into a real rate and an inflation component. Here we need r and π^e to compute i.
- Step 2: Combine the components. Under the approximation i ≈ r + π^e, the nominal rate is the sum of the real rate and the expected inflation rate.
- Step 3: Perform the calculation. If the problem provides or implies r = 2.5% and π^e = 1.6%, then i ≈ 2.5% + 1.6% = 4.1%. 
- Step 4: Round as required. The sum in this case is already to one decimal place (4.1%), so no further rounding is needed.

Notes and caveats:
- If the exact Fisher equation were used, i = (1 + r)/(1 + π^e) − 1, the result would be slightly different, especially at higher rates. For small rates, the difference is minimal and the additive approximation i ≈ r + π^e is common in introductory contexts.
- If the problem provides different inputs for r or π^e, substitute those values and compute accordingly using the same logic: add the real rate to the expected inflation rate to obtain the nominal rate, then round to the required precision.
- In absence of explicit r and π^e values, you cannot uniquely determine i; the given answer (4.1) implies specific r and π^e that sum to 4.1%.

FA25 ECON 302 002 Homework #10 (Stabilization Policy)

Using the Fisher equation, calculate the nominal interest rate 𝑖 𝑡 (in percent). Round your answer to the nearest tenth of a percent.

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