Role of money and interest rates in the economy: formula sheet

Key formulas

Functions of money

Medium of exchange + Store of value + Unit of account (+ Standard of deferred payment)

Name the function and link it to the example in the question. Deferred payment is listed separately in some texts.

Narrow money (M1), India

M1 = Currency with the public + Demand deposits with banks + Other deposits with RBI

Most liquid measure of money held by the public. Check the current RBI definition in your material.

Broad money (M3), India

M3 = M1 + Time deposits with banks

Broader and less liquid than M1, so M3 ≥ M1.

Ordering of measures

M1 ≤ M3

M0 is a different concept (the base that supports the money supply), not a subset of M1. Do not claim M0 ≤ M1 as a rule.

Money multiplier

Money multiplier = Money supply ÷ Reserve money

Shows how much money supply the banking system creates from each unit of base money.

Money demand function (general form)

Md = L(Y, r), with Md rising as Y rises and falling as r rises

Y is national income and r is the interest rate. Say this in words if asked for the general form.

Split by motive (Keynesian)

Md = L1(Y) + L2(r)

L1 covers transactions and precautionary demand and depends on income. L2 is speculative demand and depends on the interest rate.

Bond price and yield (perpetuity)

Bond price = coupon ÷ interest rate

Use this for a bond paying a fixed coupon forever. It shows why bond prices fall when interest rates rise.

Money market equilibrium

Md = Ms

The interest rate adjusts until the quantity of money demanded equals the money supply.

Velocity link (for the transactions idea)

M × V = P × Y

Here Y is real output and P the price level. This is the quantity theory, not Keynes's, but it links transactions demand to nominal income.

Simple money multiplier

m = 1 ÷ r

r is the required reserve ratio as a decimal. Assumes no cash leakage and that banks hold no excess reserves.

Maximum deposit expansion

Total new deposits = initial new reserves × (1 ÷ r)

Gives the maximum. It includes the initial deposit.

Maximum new lending

New loans created = initial deposit × (1 ÷ r) − initial deposit

Use when the question asks for loans, not deposits.

Money multiplier with cash holding

m = (1 + c) ÷ (c + r)

c = currency held by public ÷ deposits; r = reserve ratio held against deposits. Money supply = m × monetary base.

Money supply from the base

M = m × H

H is the monetary base (high-powered money): currency plus bank reserves.

Excess reserves

Excess reserves = actual reserves − required reserves

Banks can lend only the excess. Required reserves = r × deposits.

Fisher equation of exchange

MV = PT

M = money supply, V = velocity, P = price level, T = volume of transactions. An identity until V and T are assumed constant.

Income form of the equation

MV = PY

Y = real output. V here is income velocity, V = PY ÷ M. It is the usual form in exam questions.

Cambridge equation

M = kPY

k is the proportion of nominal income held as money. k = 1 ÷ V.

Price level from the theory

P = MV ÷ Y

With V and Y fixed, P changes in the same proportion as M.

Growth-rate approximation

%ΔM + %ΔV ≈ %ΔP + %ΔY

Good for small changes. With V constant: inflation ≈ money growth − real output growth.

Exact growth form

(1 + gM)(1 + gV) = (1 + gP)(1 + gY)

Use when the question gives large rates or asks for an exact figure.

Money market equilibrium

Ms = L(i, Y, P)

Ms is the money supply set by the central bank. L is liquidity preference (money demand), falling in i and rising in income Y and the price level P. The equilibrium i clears the market.

Loanable funds equilibrium

S(r) + capital inflows = I(r) + government borrowing

Saving supplies funds. Investment and government deficits demand them. In a closed economy, drop capital inflows. The equilibrium rate clears the market.

Fisher equation (approximate)

i ≈ r + πe

i is the nominal rate, r the real rate and πe expected inflation. Use for small rates.

Fisher equation (exact)

(1 + i) = (1 + r)(1 + πe)

Rearranged: r = (1 + i) ÷ (1 + πe) − 1. Use when rates or inflation are high or the question asks for an exact answer.

Ex-post real rate

r (ex post) ≈ i − π (actual)

Uses actual inflation after the event, not expected inflation.

Two-year yield from a forward rate (annual compounding)

(1 + y₂)² = (1 + y₁) × (1 + f₁,₂)

y₁ and y₂ are the 1-year and 2-year spot yields. f₁,₂ is the forward rate for year 2, agreed today.

Forward rate from spot yields

f₁,₂ = (1 + y₂)² ÷ (1 + y₁) − 1

Rearranged form of the rule above. Use decimals in the working.

General n-year spot yield

(1 + yₙ)ⁿ = (1 + y₁)(1 + f₁,₂)(1 + f₂,₃)…(1 + fₙ₋₁,ₙ)

Holds by no-arbitrage. Gives the long yield as a geometric average of forward rates.

Pure expectations theory

f₁,₂ = E[ y₁ in one year ]

The forward rate equals the expected future short rate. The long yield is an average of expected short rates.

Liquidity preference theory

f₁,₂ = E[ y₁ in one year ] + L, where L > 0

L is the liquidity or term premium. Forward rates overstate expected future short rates.

Shape rule

Normal: yₙ rises with n. Inverted: yₙ falls with n. Flat: yₙ is about constant.

Describe the shape using the yields given, not just the label.

Real interest rate (approximate)

r ≈ i − π

i is the nominal rate and π is expected inflation. Spending decisions respond mainly to the real rate. The exact form is (1 + r) = (1 + i) ÷ (1 + π).

Aggregate demand identity

AD = C + I + G + (X − M)

Use it to say which component each channel affects: interest rate channel hits C and I, exchange rate channel hits X − M.

Interest rate channel chain

Policy rate ↓ → lending rates ↓ → C and I ↑ → AD ↑ → output ↑ and inflation ↑

Reverse every sign for a rate rise. Mention lags.

Exchange rate channel chain

Policy rate ↓ → capital outflow → currency ↓ → X ↑, M ↓ → AD ↑

Holds in general when other things are equal. Other factors also move exchange rates.

Quantity theory link

M × V = P × Y

Used to link money growth to prices. It assumes V and Y are stable, which may not hold in the short run.

Quick revision

• Money functions: medium of exchange, unit of account, store of value, standard of deferred payment.
• Liquidity preference: people hold money for transactions, precaution and speculation.
• A higher interest rate raises the opportunity cost of holding money, so money demand falls.
• Higher income shifts the money demand curve right; a higher interest rate moves you along it.
• Simple deposit multiplier = 1 ÷ reserve ratio, assuming no cash leakage and all lending is redeposited.
• Quantity theory: M × V = P × T (or P × Y), with M the money supply, V velocity and P the price level.
• Strict quantity theory assumes V and real output are stable, so money growth leads to inflation.
• The interest rate is where money supply equals money demand; extra supply lowers it.
• Yield curve theories: expectations, liquidity preference and market segmentation.
• An upward-sloping curve is often explained by expected rate rises plus a liquidity premium.
• Policy rate change passes through bank rates, credit, asset prices, exchange rate and expectations.
• Tighter policy aims to cut demand and inflation but can slow growth and employment.

Common mistakes

• Saying money has value only because it is made of a valuable material. Fix: State that fiat money has value because of legal tender status and public trust, not its material.
• Mixing up store of value and unit of account. Fix: Store of value is about holding purchasing power over time. Unit of account is about measuring and quoting prices.
• Saying a rise in the interest rate shifts the money demand curve left. Fix: The interest rate is on the vertical axis. Its change is a movement along the curve. Only other factors, such as income, shift it.
• Linking the speculative motive to income. Fix: Remember the pairing: transactions and precautionary go with income, speculative goes with the interest rate.
• Using the multiplier as 1 × r instead of 1 ÷ r. Fix: Check the direction: a smaller reserve ratio must give a larger multiplier.
• Giving total deposits when the question asks for new loans. Fix: Loans created = total deposit expansion − initial deposit. Read the question wording.
• Treating MV = PT as a proven law that always holds as a causal statement. Fix: Say that it is true by definition. It only gives a theory of inflation when V and T are assumed stable and causation runs from M to P.
• Forgetting that real output growth reduces inflation. Fix: Use inflation ≈ money growth + velocity change − output growth. Keep Y in the working.
• Drawing money supply as upward sloping when the central bank sets it Fix: In the standard liquidity preference diagram, the central bank fixes money supply, so draw it vertical. Say so explicitly.
• Confusing a shift of money demand with a movement along it Fix: A change in the interest rate moves you along the curve. A change in income or prices shifts the curve. Name the cause before drawing.

Exam tips

• Learn the three functions with a one-line example each. Multiple-choice questions often describe a scenario and ask you to pick the function.
• In written answers, define the term first, then apply it. Marks usually go for definition and application.
• Write out the components of M1 and M3 from memory. Calculation questions are easy if you know them.
• Mention a limitation, such as inflation hurting store of value, to earn evaluation marks.
• Use the definitions in your IAI study material if they differ slightly from other sources.
• Always name all three motives and pair each with its driver. This is the standard marking point.
• Draw the diagram when asked: interest rate on the vertical axis, quantity of money on the horizontal axis, a downward-sloping curve. Label the axes and show shifts clearly.
• In MCQs, the trap is usually movement versus shift. Check the variable on the axis first.