To determine the correct money multiplier given a reserve rate [tex]\( r = 0.12 \)[/tex], we follow these steps:
1. Understanding the Money Multiplier:
The money multiplier [tex]\( m \)[/tex] is calculated based on the reserve rate. The money multiplier is the inverse of the reserve rate. Mathematically, it is represented as:
[tex]\[
m = \frac{1}{r}
\][/tex]
2. Substitute the Reserve Rate:
Here, the reserve rate [tex]\( r \)[/tex] is given as 0.12. We substitute this value into the formula for the money multiplier:
[tex]\[
m = \frac{1}{0.12}
\][/tex]
3. Calculate the Money Multiplier:
Performing the division, we find:
[tex]\[
\frac{1}{0.12} = 8.333333333333334
\][/tex]
4. Evaluate the Options:
Let's examine the given options to find a match:
- A. [tex]\( 10 \cdot 0.12 \)[/tex] results in [tex]\( 1.2 \)[/tex] (incorrect).
- B. [tex]\( 0.12^2 \)[/tex] results in [tex]\( 0.0144 \)[/tex] (incorrect).
- C. [tex]\(\frac{1}{0.12}\)[/tex] results in [tex]\( 8.333333333333334 \)[/tex] (correct).
- D. [tex]\(\frac{1}{0.12^2}\)[/tex] results in [tex]\( \frac{1}{0.0144} = 69.44444444444444 \)[/tex] (incorrect).
Therefore, the correct answer is C. [tex]\(\frac{1}{0.12}\)[/tex], which simplifies to [tex]\( 8.333333333333334 \)[/tex].
