Answer:
C.$48,000,000; $54,000,000
Step-by-step explanation:
First we lay out the data
Currency (C) = $6,000,000
Reserves (R) = $6,000,000
Reserve-Deposit Ratio (rr) = 12.5%
To find deposits we simply solve a rule of three. Reserves are 12.5% of what deposits are:
X 100%
6,000,000 12.5%
6,000,000 x 100/12.5 = 48,000,000
So Deposits (D) are $ 48,000,000
Now, to find the money supply, we must solve this equation
M = m x B
Where M = Money supply, m = money multiplier and B = monetary base
Monetary base is equal to currency in hands of the public + reserves, so:
B = C + R
B = $6,000,000 + $6,000,000
B = $12,000,000
The money multiplier equals to
m = (cr + 1)/(cr + rr)
cr is currency - deposit ratio
In this case currency is $6,000,000 and deposits are $48,000,000, so the currency-deposit ratio (cr) is the same as the reserve-deposit ratio (rr) = 12.5%
Now we plug the amounts into the formula, remember that we must convert percentages into decimals when solving an equation:
m = (0.125 + 1) / (0.125 + 0.125)
m = 4.5
Finally, we can solve for the money supply. Money supply is equal to the monetary multiplier times the monetary base:
M = m x B
M = 4.5 x $12,000,000
M = $54,000,000