At one time, the country of Freedonia had no banks, but had currency of $40 million. Then a banking system was established with a reserve requirement of one-third. The people of Freedonia now keep half their money in the form of currency and half in the form of bank deposits. If banks do not hold excess reserves, how much currency do the people of Freedonia now hold?
A) $13.33 million
B) $20 million
C) $33.34 million
D) $36.36 million

Question

Quizplus · Accepted Answer

Initially, the country had $40 million in currency. When the banking system was established with a reserve requirement of one-third, banks were required to keep $40 million/3 = $13.33 million as reserves and could lend out the rest, which is $26.67 million. 
Now, the people of Freedonia keep half of their money ($40 million) as currency, which is $20 million, and the other half in the form of bank deposits. Since banks do not hold excess reserves, all the deposits made by people will have been lent out by banks. Hence, the amount of money in the form of bank deposits is $26.67 million (as calculated above). 
Therefore, the total amount of money in the economy is $20 million (currency) + $26.67 million (bank deposits) = $46.67 million. 
Since the people now hold half of their money in the form of currency, the amount of currency they hold is $46.67 million/2 = $23.33 million. 
However, this is the total amount of currency in the economy, which includes the reserves held by banks. Therefore, to find out how much currency people hold, we need to subtract the reserves held by banks, which is $13.33 million. Hence, the currency held by people is $23.33 million - $13.33 million = $10 million. 
Therefore, the people of Freedonia now hold $10 million in currency. The closest option is C) $33.34 million, which is the total amount of money in the economy if people still held all their money in the form of currency (which is not the case).

At One Time, the Country of Freedonia Had No Banks