The question is as follows: In a simple close economy, banks are required to maintain a liquidity ratio of 8%. An additional £15 billion of currency is deposited in the banking system. Calculate the bank multiplier and hence the increase in the total amount of deposits.
I am having trouble finding out how to calculate the bank multiplier. Please help.
If you define the liquidity ratio as the minimum fraction of customer deposits and notes that each commercial bank must hold as reserves then the liquidity ratio is $\frac{R}{D}$ where
$R$ is the "actual" currency reserves (notes and coins physically held by banks) and $D$ is the amount credited to customers in the form of deposits.
The bank multiplier is just $\frac{D}{R}$ i.e., n your case $\frac{1}{0.08}$ = 12.5.
So an extra £15 bn currency can multply into an extra $15 bn * 12.5 of deposits.
Put another way the liquidity ratio will continue to be $\frac{15 * 0.08}{15}$.