How are the reserve ratio and the deposit multiplier linked?

They are reciprocals: a ratio of 20 percent gives a multiplier of 5, and a higher ratio means a smaller multiplier.

Why is real deposit creation usually less than 1 divided by the reserve ratio?

Because the public may hold cash outside banks and banks may hold excess reserves, and both pull the multiplier down.

S5 Economics Money and Banking Paper 4: Reserves, Money Supply and Prices

2026-11-03

S · 5

Paper 4 targets the multiplier and reserve ratio in both directions, real interest and purchasing power, and adds the equation of exchange and open market operations.

Quick answer　At a 10 percent reserve ratio a deposit of 6 000 dollars leaves 600 in reserves and 5 400 to lend; a multiplier of 8 means a reserve ratio of 12.5 percent.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10 questions
Suggested time	25 minutes
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Money and Banking
Level	S5

02　Questions (10 items)

FoundationThe reserve ratio is 10 percent and a customer deposits 6 000 dollars. How much must be kept as reserves and how much can be lent?
FoundationThe deposit multiplier is 8. What is the reserve ratio?
FoundationThe nominal rate is 7 percent and inflation 2.5 percent. What is the real rate?
FoundationThe public holds 400 billion dollars of cash and 1 100 billion in current deposits. What is M1?
IntermediateBanks hold 900 billion dollars of reserves and the reserve ratio is 15 percent. What is the maximum total of deposits?
IntermediateA person holds 10 000 dollars in cash and inflation is 4 percent. What is that money worth in today prices after one year?
IntermediateMoney supply is 400 billion dollars, velocity is 5 and real output is 1 000 billion. Using the equation of exchange, what is the price level?
ChallengeThe central bank sells 500 billion dollars of bonds in the open market and the reserve ratio is 12.5 percent. By how much can the money supply contract at most?
ChallengeThe nominal rate is 9 percent and inflation 5 percent. Work out the real rate precisely.
Error redoSomeone claims that when the money supply rises, prices must rise at once. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	Reserves of 600 dollars and 5 400 dollars to lend.	6 000 times 0.1 gives 600, leaving 5 400 dollars to lend.
2	12.5 percent.	The reserve ratio is 1 divided by the multiplier, that is 1 over 8, giving 0.125.
3	4.5 percent.	The real rate is roughly the nominal rate minus inflation, that is 7 minus 2.5 percent.
4	M1 is 1 500 billion dollars.	M1 counts cash and current deposits only: 400 plus 1 100 gives 1 500 billion dollars.
5	6 000 billion dollars.	Deposits equal reserves divided by the reserve ratio, that is 900 over 0.15.
6	About 9,615.38 dollars.	Purchasing power equals 10 000 divided by 1.04, about 9,615.38 dollars.
7	2.0.	MV equals PY: 400 times 5 gives 2 000, and dividing by 1 000 gives 2.0.
8	By up to 4 000 billion dollars.	The multiplier is 1 over 0.125, which is 8; 500 times 8 gives 4 000 billion dollars.
9	About 3.81 percent.	The precise real rate is 1.09 over 1.05 minus 1, giving 0.0381, that is 3.81 percent.
10	It ignores real output and velocity: if output rises at the same time, or the extra money is simply held, prices need not rise at once.	By MV equals PY, what happens to prices depends on output and velocity as well.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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