To determine the resulting money multiplier when the reserve rate is set to 2%, we can use the money multiplier formula. The money multiplier is inversely related to the reserve rate, which means that the formula to calculate it is:
[tex]\[ \text{Money Multiplier} = \frac{1}{\text{Reserve Rate}} \][/tex]
Step-by-Step Solution:
1. Identify the reserve rate: In this problem, the Federal Reserve has set the reserve rate to 2%.
2. Convert the reserve rate to a decimal: The reserve rate of 2% needs to be converted from a percentage to a decimal to use in the formula.
[tex]\[
\text{Reserve Rate} = \frac{2}{100} = 0.02
\][/tex]
3. Apply the money multiplier formula: Substitute the decimal form of the reserve rate into the formula.
[tex]\[
\text{Money Multiplier} = \frac{1}{0.02}
\][/tex]
4. Calculate the money multiplier:
[tex]\[
\frac{1}{0.02} = 50.0
\][/tex]
Therefore, when the Federal Reserve sets the reserve rate to 2%, the resulting money multiplier is 50.0.
