Question

Imagine Federal Reserve Chairman Janet Yellen discovering a secret room in her office and finding $195 million stashed away during the Volcker era, when inflation "was more of a concern." Suppose she decides to expand the money supply by depositing the whole $195 million in one commercial bank Now assume the following . The reserve ratio is 9.50% for all commercial banks Banks are fully loaned up initially. Any bank that has excess reserves will loan the entire amount of those excess reserves to one borrower, who will spend it all in one place, and the recipient will then deposit the entire amount in one bank How many loans would it take the banking system to create one billion dollars out of the money injection? Number loans

Answer 1

The deposit of entire $195 million will increase the excess reserves with the bank by $195 million.

So,

Excess reserves created with the bank will be $195 million.

This bank will lend its entire excess reserves of $195 billion.

So, first loan will be of $195 billion.

This will be spent and then deposited in another bank.

Following table shows the number of loans needed to make $1 billion out of the money injection -

Number of loans	Reserves (A)	Required Reserves (B)	Loan amount (A - B)
1	$195 million	$0 million	$195 million
2	$195 million	$18.53 million	$176.47 million
3	$176.47 million	$16.76 million	$159.71 million
4	$159.71 million	$15.17 million	$144.54 million
5	$144.54 million	$13.73 million	$130.08 million
6	$130.08 million	$12.43 million	$117.65 million
7	$117.65 million	$11.17 million	$106.48 million

The above table shows that after seven loans being made, total money created by banking system is approximately $1,029.93 million.

So,

It would take 7 loans for the banking system to create one billion dollars out of the money injection.