To determine the money multiplier given a reserve rate [tex]\( r = 0.12 \)[/tex], we need to understand the concept of the money multiplier. The money multiplier is defined as the reciprocal of the reserve rate.
Let's analyze each of the given options to see which one correctly represents the money multiplier:
1. Option A: [tex]\( 0.12^2 \)[/tex]
Here, we raise the reserve rate [tex]\( r \)[/tex] to the power of 2:
[tex]\[
r^2 = (0.12)^2 = 0.0144
\][/tex]
2. Option B: [tex]\( \frac{1}{0.12} \)[/tex]
For this option, we take the reciprocal of the reserve rate:
[tex]\[
\frac{1}{r} = \frac{1}{0.12} \approx 8.333333333333334
\][/tex]
3. Option C: [tex]\( 10 \cdot 0.12 \)[/tex]
Here, we multiply the reserve rate by 10:
[tex]\[
10 \cdot r = 10 \cdot 0.12 = 1.2
\][/tex]
4. Option D: [tex]\( \frac{1}{0.12^2} \)[/tex]
For this option, we take the reciprocal of the square of the reserve rate:
[tex]\[
\frac{1}{r^2} = \frac{1}{(0.12)^2} = \frac{1}{0.0144} \approx 69.44444444444444
\][/tex]
Given these calculations, the correct money multiplier is found in Option B: [tex]\( \frac{1}{0.12} \)[/tex], which gives us approximately 8.333333333333334.
Thus, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]
