This question does not follow from 22 e) above. This is an independent question. 22 f) Suppose that the monetary authority sets the real interest rate using the rule: r = 0.02 + 0.5 (π – π*), where π is the inflation rate and π* is the inflation target. Suppose that current inflation rate (π) is 6% (or 0.06) and the inflation target (π*) is 2% (or 0.02). What is the nominal interest rate? Write your answer in _______ %. For example, if 7%, just enter 7.
Question
This question does not follow from 22 e) above. This is an independent question. 22 f) Suppose that the monetary authority sets the real interest rate using the rule: r = 0.02 + 0.5 (π – π*), where π is the inflation rate and π* is the inflation target. Suppose that current inflation rate (π) is 6% (or 0.06) and the inflation target (π*) is 2% (or 0.02). What is the nominal interest rate? Write your answer in _______ %. For example, if 7%, just enter 7.
Solution
To find the nominal interest rate, we first need to calculate the real interest rate (r) using the given rule: r = 0.02 + 0.5 (π – π*).
Step 1: Substitute the given values into the equation. r = 0.02 + 0.5 (0.06 - 0.02)
Step 2: Simplify the equation within the parentheses. r = 0.02 + 0.5 (0.04)
Step 3: Multiply 0.5 by 0.04. r = 0.02 + 0.02
Step 4: Add 0.02 and 0.02. r = 0.04
So, the real interest rate is 0.04 or 4%.
The nominal interest rate is the sum of the real interest rate and the inflation rate.
Step 5: Add the real interest rate and the inflation rate. Nominal interest rate = r + π Nominal interest rate = 0.04 + 0.06
Step 6: Simplify the equation. Nominal interest rate = 0.10
So, the nominal interest rate is 0.10 or 10%.
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