ANSWER-- $9.57 million

As Federal buys bonds worth $11 million , the dealer's account is credited by $11 million. Hence, the dealer's bank receives a deposit of $11 million.

Required reserves are a certain percentage of the deposits of the bank which it is required to keep with itself in the form of reserves. These reserves cannot be used by the bank to extend loans and advances. The reserves which are over and above the required reserves, called excess reserves, are used to make loans and advances.

As the dealer's bank will receive $11 million deposits, the bank will keep 13% of this deposit as required reserves and will loan out the excess reserves. So,

Required reserves= deposits x required reserve ratio

Required reserves= $11 million x 13%

Required reserves= $11 million x 13/100

Required reserves= $11 million x 0.13

Required reserves= $1.43 million

As such, the dealer's bank will keep required reserves of $1.43 million out of deposit received of $11 million and will loans out it's excess reserves. As out of deposit of $11 million, required reserves are $1.43 million, the rest of amount of deposit which is over and above the required reserves ( excess reserves) will be lent out

Excess reserves= deposits - required reserves

Excess reserves= $11 million - $1.43 million

Excess reserves= $9.57 million

As such, following the Federal's purchase, the bank will be able to lent to it's customers $9.57 million ( ANSWER)