Let [tex]$r=0.07$[/tex] be the reserve rate. Which of the following is the money multiplier?

A. [tex]$10 \cdot 0.07$[/tex]
B. [tex][tex]$\frac{1}{0.07^2}$[/tex][/tex]
C. [tex]$0.07^2$[/tex]
D. [tex]$\frac{1}{0.07}$[/tex]



Answer :

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]