To determine the money multiplier when the reserve rate [tex]\( r \)[/tex] is given, we use the formula for the money multiplier:
[tex]\[ \text{Money Multiplier} = \frac{1}{r} \][/tex]
Given that the reserve rate [tex]\( r \)[/tex] is [tex]\( 0.07 \)[/tex], we substitute this value into the formula:
[tex]\[ \text{Money Multiplier} = \frac{1}{0.07} \][/tex]
Upon calculating this value, we obtain:
[tex]\[ \text{Money Multiplier} = 14.285714285714285 \][/tex]
Now, let's analyze each of the given options:
A. [tex]\( 10 \cdot 0.07 \)[/tex]
[tex]\[ 10 \cdot 0.07 = 0.70 \][/tex]
B. [tex]\( \frac{1}{0.07^2} \)[/tex]
[tex]\[ 0.07^2 = 0.0049 \][/tex]
[tex]\[ \frac{1}{0.0049} \approx 204.08 \][/tex]
C. [tex]\( 0.07^2 \)[/tex]
[tex]\[ 0.07^2 = 0.0049 \][/tex]
D. [tex]\( \frac{1}{0.07} \)[/tex]
[tex]\[ \frac{1}{0.07} \approx 14.285714285714285 \][/tex]
From the comparisons, it is evident that option D, [tex]\( \frac{1}{0.07} \)[/tex], matches the calculated value of the money multiplier.
Therefore, the correct answer is:
D. [tex]\( \frac{1}{0.07} \)[/tex]
