Sure! Let's solve this problem step-by-step, focusing on understanding how changes in the reserve rate affect the money supply through the process of fractional-reserve banking.
### Step 1: Understand Money Multiplier
The money multiplier ([tex]\( MM \)[/tex]) is a formula used to determine the total amount of money that the banking system generates with each dollar of reserves. It is given by:
[tex]\[ MM = \frac{1}{\text{Reserve Requirement}} \][/tex]
### Step 2: Calculate the Initial Money Multiplier
The initial reserve requirement is 5%, or 0.05.
[tex]\[
MM_{\text{initial}} = \frac{1}{0.05} = 20
\][/tex]
### Step 3: Calculate the New Money Multiplier
The new reserve requirement is 2.5%, or 0.025.
[tex]\[
MM_{\text{new}} = \frac{1}{0.025} = 40
\][/tex]
### Step 4: Calculate Initial Money Creation
Let's see how much money is created initially with an initial deposit of [tex]$35,000.
\[
\text{Total Money Created (initial)} = \text{Initial Deposit} \times MM_{\text{initial}}
\]
\[
\text{Total Money Created (initial)} = 35,000 \times 20 = 700,000
\]
### Step 5: Calculate New Money Creation
Next, calculate the total money created with the new reserve rate.
\[
\text{Total Money Created (new)} = \text{Initial Deposit} \times MM_{\text{new}}
\]
\[
\text{Total Money Created (new)} = 35,000 \times 40 = 1,400,000
\]
### Step 6: Calculate the Increase in Amount of Money Created
Finally, let's find out the increase in the amount of money created due to the change in the reserve rate.
\[
\text{Increase in Money Created} = \text{Total Money Created (new)} - \text{Total Money Created (initial)}
\]
\[
\text{Increase in Money Created} = 1,400,000 - 700,000 = 700,000
\]
### Conclusion
The decrease in the reserve rate from 5% to 2.5% increases the amount of money created through fractional-reserve banking from an initial deposit of $[/tex]35,000 by [tex]$700,000.
Thus, the correct answer is:
B. It increases the amount by $[/tex]700,000.
