The reserve ratio is 10%, which means that the bank is required to hold 10% of checkable deposits as reserves. Given that the checkable deposits are $100,000, the required reserves are:
10% x $100,000 = $10,000
Since the bank already has reserves of $10,000, this means that it has met its reserve requirement before the deposit.
Now, when the households deposit $20,000 in currency, the bank adds that currency to its reserves, which means that its total reserves are now:
$10,000 (original reserves) + $20,000 (newly deposited currency) = $30,000
The excess reserves are the amount of reserves that the bank holds above its required reserve amount. In this case, the required reserves are $10,000, so the excess reserves are:
$30,000 (total reserves) - $10,000 (required reserves) = $20,000
Therefore, the bank now has $20,000 in excess reserves.