The formulas used in the calculations are:
\[ \text{Inflation Rate Gap} = \text{Current Inflation Rate} - \text{Desired Inflation Rate} \]
\[ \text{Output Gap} = \log(\text{Current GDP}) - \log(\text{Long-run GDP}) \]
\[ \text{Real Interest Rate} = \text{Nominal Interest Rate} - \text{Current Inflation Rate} \]
\[ \text{Federal Funds Target Rate} = \text{Real Interest Rate} + \text{Current Inflation Rate} \\ + 0.5 \times \text{Inflation Rate Gap} + 0.5 \times \text{Output Gap} \]
This calculator computes the federal funds target rate using the Taylor rule based on the input values of current inflation rate, current GDP, long-run GDP, and nominal interest rate.
Let's assume the following:
Calculate the inflation rate gap:
\[ \text{Inflation Rate Gap} = 4\% - 2\% = 2\% \]
Calculate the output gap:
\[ \text{Output Gap} = \log(2,000,000,000) - \log(3,000,000,000) = 9.30 - 9.48 = -0.18\% \]
Calculate the real interest rate:
\[ \text{Real Interest Rate} = 5\% - 4\% = 1\% \]
Calculate the federal funds target rate:
\[ \text{Federal Funds Target Rate} = 1\% + 4\% + 0.5 \times 2\% + 0.5 \times (-0.18\%) = 5.91\% \]