To determine the money multiplier given the reserve rate [tex]\( r = 0.05 \)[/tex], we can follow these steps:
1. Understand the formula for the money multiplier: The money multiplier ([tex]\( M \)[/tex]) is the inverse of the reserve rate ([tex]\( r \)[/tex]). Mathematically, this can be expressed as:
[tex]\[
M = \frac{1}{r}
\][/tex]
2. Calculate the money multiplier: Substitute the given reserve rate ([tex]\( r = 0.05 \)[/tex]) into the formula:
[tex]\[
M = \frac{1}{0.05}
\][/tex]
Simplify this fraction:
[tex]\[
M = \frac{1}{0.05} = 20
\][/tex]
3. Compare the calculated money multiplier to the provided options:
- Option A: [tex]\( 10 \cdot 0.05 = 0.5 \)[/tex]
- Option B: [tex]\( \frac{1}{0.05^2} = \frac{1}{0.0025} = 400 \)[/tex]
- Option C: [tex]\( \frac{1}{0.05} = 20 \)[/tex]
- Option D: [tex]\( 0.05^2 = 0.0025 \)[/tex]
The correct option matches our calculated value, which is 20.
Therefore, the correct answer is:
[tex]\[
\boxed{\text{C}}
\][/tex]
