Assume the reserve requirement is 10%. first national bank receives a deposit of $5,400. if there is no slippage, how much could the money supply expand?

The core of the question is the money multiplier. assuming first national receives $5,400, the bank has to keep 10% * $5400 = $540 because of the reserve requirement and can lend the remaining $5400-$540= $4860. Now this money goes to circulation again and the next step is analogous: 10%* $4860= $486 have to be kept as a reserve requirement and the remaining $4860 - $486= $4374 are circulated back into the economy. i can go on forever adding up the money that will go into the economy and hence expand the money supply ($4860+ $4374 + ... ) , but there is a simple mathematical formula that makes my life easier: it is called a geometric series. in our case $5400 + $4860 + $4374 +... is abbreviated to$5400∗(1+0.9+0.92+..)and the term in the brackers is the geometric series11−0.9which equals 10. This is the power of money. your answer is that with a deposit of $5400 the money supply increases by $5400 * 10 = $54 000.