To solve for the money multiplier, we use the given reserve rate [tex]\( r = 0.05 \)[/tex]. The formula for the money multiplier is given by:
[tex]\[ \text{Money Multiplier} = \frac{1}{r} \][/tex]
Let's evaluate each of the given options to identify which one matches this formula:
A. [tex]\( 10 \cdot 0.05 \)[/tex]
Calculating this, we get:
[tex]\[ 10 \cdot 0.05 = 0.5 \][/tex]
B. [tex]\( \frac{1}{0.05^2} \)[/tex]
Calculating this, we get:
[tex]\[ 0.05^2 = 0.0025 \][/tex]
[tex]\[ \frac{1}{0.0025} = 400 \][/tex]
C. [tex]\( \frac{1}{0.05} \)[/tex]
Calculating this, we get:
[tex]\[ \frac{1}{0.05} = 20 \][/tex]
D. [tex]\( 0.05^2 \)[/tex]
Calculating this, we get:
[tex]\[ 0.05^2 = 0.0025 \][/tex]
From our calculations, option C is the correct one:
C. [tex]\( \frac{1}{0.05} \)[/tex]
The numerical result of this calculation confirms that the money multiplier is [tex]\( 20 \)[/tex].
