How to calculate Excess reserves, Required reserves and required reserve ratio

When analysing problems of such nature, it is good to distinguish between the two types of banks:


Central bank - The Central bank control the money supply within the economy.


Commercial banks - They provide facilities for customers to lend and save money.


First, we will outline some definitions and then go over some examples to solidify the concepts.


Required reserves - The amount of cash deposits that the bank must keep on the premises.


Required reserve ratio - This is the ratio of required reserves to total deposits and is defined


\text{Required reserve ratio} = \frac{\text{Required reserves}}{\text{Total Deposits}}


The required reserve ratio is typically set by the central bank of a country and is put in place so that banks will have enough money if people wish to withdraw their deposits.


Excess reserves - Excess reserves are reserves held in addition to required reserves.


Example 1 - Calculate the required reserves


Suppose that the central bank has stipulated that the required reserve ratio is 10% and a commercial bank has $1,000 deposited in it by its customers. Calculate the Required reserves.


This is telling us that the commercial bank needs to keep 10% of its deposits as required reserves, therefore:


\text{Required reserves} = 0.1*1000 = $100


The required reserves in this case are $100 and the bank is able to lend out the remaining $900.


Example 2 - Calculate the excess reserves


Suppose in the previous example that the bank decided to keep $200 of the deposits as reserves. How much would the Excess reserves be? We have


\text{Excess reserves = Total reserves - required reserves}


We know from the previous example that the required reserves are $100, so we have

\text{Excess reserves} = $200 - $100 = $100


Example 3 - Calculate the required reserve ratio


Suppose that a bank is not holding onto any excess reserves and they currently have a total of $10,000 deposits and have $400 as reserves. What is their reserve ratio?


\text{Required Reserve ratio} = \frac{400}{10,000} = 0.04


Therefore, the required reserve ratio is 4%.