Business Economics · Balance of payments and exchange rates

Purchasing Power Parity and Interest Rate Parity Explained

Updated 11 October 2026 · Fact-checked

Purchasing power parity (PPP) says exchange rates move to offset price differences between countries, so a basket costs the same everywhere. Interest rate parity says exchange rate changes offset interest rate differences. To solve questions, define the rate quote, apply the formula, and check which currency is at a premium or discount.

Understand Purchasing Power Parity and Interest Rate Parity

Exchange rates need a theory. Two simple ideas link them to other prices. One uses goods prices. The other uses interest rates.

Purchasing power parity (PPP) starts from the law of one price. If the same good sells in two countries and trade is free and costless, its price should be equal once converted into one currency. If it were cheaper in India, buyers would purchase it there and push its price up. The exchange rate would also adjust. Absolute PPP applies this to a whole basket of goods. Relative PPP is weaker and more useful. It says the exchange rate changes by about the difference in inflation rates. The country with higher inflation sees its currency weaken.

PPP often fails in the short run. Goods are not identical, transport costs and tariffs exist, and many items (haircuts, rent) are not traded. Capital flows and speculation also move exchange rates faster than prices. PPP is better seen as a long-run anchor.

The nominal exchange rate is the market price of one currency in another, for example ₹ per US dollar. The real exchange rate adjusts for price levels. It measures the price of foreign goods in terms of domestic goods, that is, how many baskets of domestic goods you need to buy one basket of foreign goods. If PPP holds exactly, the real exchange rate is constant. A real rate that rises or falls shows a change in competitiveness.

Interest rate parity (IRP) links the spot rate, the forward rate and interest rates. Covered interest parity says you cannot make riskless profit by borrowing in one currency, converting, investing abroad, and locking in the forward rate. So the forward rate must reflect the interest differential. The currency with the higher interest rate trades at a forward discount. Uncovered interest parity has no forward contract. It says the expected change in the spot rate equals the interest differential. It carries exchange rate risk, so it is a statement about expectations, and it often fails in practice.

Key rules to remember

Law of one price: P(domestic) = S × P(foreign); S is the domestic price of one unit of foreign currency (for example ₹ per US$). Holds for a tradable good with no transport costs or barriers.
Absolute PPP: S = P(domestic basket) ÷ P(foreign basket); Same quote as above. Assumes identical baskets. Rarely holds exactly.
Relative PPP (approximate): % change in S ≈ inflation(domestic) − inflation(foreign); A higher domestic inflation rate means the domestic currency depreciates (S rises).
Relative PPP (exact): S1 = S0 × (1 + i_d) ÷ (1 + i_f); i_d and i_f are domestic and foreign inflation over the period. S0 is the starting rate.
Real exchange rate: R = S × P(foreign) ÷ P(domestic); S is domestic currency per unit of foreign currency. A rise in R means domestic goods are cheaper relative to foreign goods (more competitive). R is constant if PPP holds.
Covered interest parity: F = S × (1 + i_d) ÷ (1 + i_f); F is the forward rate, quoted as domestic currency per unit of foreign currency, for the same period as the interest rates. Higher domestic rate means forward premium for the foreign currency.
Uncovered interest parity: E(S1) = S0 × (1 + i_d) ÷ (1 + i_f); Uses the expected future spot rate. Approximately: expected % change in S ≈ i_d − i_f.

How to solve Purchasing Power Parity and Interest Rate Parity questions

Use this order for any PPP or IRP question. Most lost marks come from quoting the rate the wrong way round.

1Write the quote convention. Decide which currency is the home currency and write S as home currency per one unit of foreign currency.
2Identify which theory is asked: PPP (prices or inflation) or IRP (interest rates), and whether it is covered (forward rate) or uncovered (expected spot).
3Write the formula with i_d on top and i_f below for the same time period. Use the same period for rates and for the exchange rate horizon.
4Substitute the numbers. Convert percentages to decimals and compute exactly unless the question asks for an approximation.
5Interpret the direction: higher inflation or higher interest rate in the home country means the home currency is weaker (S higher) under PPP, or at a forward discount under IRP.
6For real versus nominal questions, compute the real rate with R = S × P(foreign) ÷ P(domestic) and say what the change means for competitiveness.
7State the assumptions and comment on why the theory may fail in practice (transport costs, non-traded goods, risk premia, capital controls).

Quickest way: Rate-over-rate shortcut

When to use it: Use it for multiple-choice questions and quick numerical parts where you need the future rate or forward rate fast.

Put the home currency per unit of foreign currency as S.
Multiply S by (1 + home rate) ÷ (1 + foreign rate). The rate is inflation for PPP or interest for IRP.
Sanity check: if the home rate is higher, the answer must be higher than S.
If the question allows, the approximation S × (1 + difference) gives a close value. Use the exact form when options are close together.

Common mistakes in Purchasing Power Parity and Interest Rate Parity

Inverting the exchange rate quote, so the answer moves the wrong way.
Quotes such as ₹/US$ and US$/₹ look similar and questions switch between them.
Fix: Write the quote at the start. If S is foreign per home currency, the ratio in the formula flips to (1 + i_f) ÷ (1 + i_d).
Saying a higher interest rate means the currency strengthens in the forward market.
Students think high rates attract capital, which is true for spot demand, but this is not what parity says.
Fix: Under covered parity the high interest rate currency trades at a forward discount, which removes the gain from the extra interest.
Treating PPP as always true.
The formulas look exact.
Fix: Say PPP is a long-run tendency. Give reasons it fails: non-traded goods, transport costs, tariffs, different baskets, and capital flows.
Mixing periods, such as annual interest rates with a six-month forward rate.
The question gives annual rates and a shorter horizon.
Fix: Convert rates to the period of the forward contract before applying the formula, for example 6-month rate = annual rate ÷ 2 for simple interest.
Confusing covered and uncovered parity.
Both use the same interest ratio.
Fix: Covered uses the forward rate F and is a no-arbitrage result. Uncovered uses the expected spot rate and carries risk.
Reading the real exchange rate as the nominal rate adjusted for interest.
The word 'real' appears in real interest rates too.
Fix: Real exchange rate adjusts for price levels, not interest rates. It compares the cost of goods across countries.

Worked examples

Example 1

The exchange rate is ₹80 per US$. Over the next year, inflation is expected to be 6% in India and 2% in the US. Using relative PPP, find the expected exchange rate after one year.

Show the solution

Quote: S0 = ₹80 per US$, so India is the home country.
Apply S1 = S0 × (1 + i_d) ÷ (1 + i_f).
S1 = 80 × 1.06 ÷ 1.02.
1.06 ÷ 1.02 = 1.039216 (to 6 decimals).
S1 = 80 × 1.039216 = 83.137.
Interpretation: higher Indian inflation weakens the rupee.

Answer: About ₹83.14 per US$ (the rupee depreciates by about 3.9%).

Example 2

The spot rate is ₹80 per US$. One-year interest rates are 7% in India and 3% in the US. (a) Find the one-year forward rate consistent with covered interest parity. (b) Which currency is at a forward discount?

Show the solution

Quote: ₹ per US$, India is home. i_d = 0.07, i_f = 0.03.
Apply F = S × (1 + i_d) ÷ (1 + i_f).
F = 80 × 1.07 ÷ 1.03.
1.07 ÷ 1.03 = 1.038835.
F = 80 × 1.038835 = 83.107.
F is higher than S, so more rupees are needed per dollar in a year.
So the rupee is at a forward discount and the dollar at a forward premium.

Answer: (a) About ₹83.11 per US$. (b) The rupee trades at a forward discount, because India has the higher interest rate.

Exam tips

Write the quote convention (₹ per US$) as your first line. Examiners award marks for a consistent setup.
Expect a short written question asking why PPP fails. Give three distinct reasons, not one repeated.
For real versus nominal questions, explain what a change in the real exchange rate means for exports and imports.
In covered versus uncovered parity answers, name the difference: forward contract and no risk versus expected spot and risk.
Show the formula in your working even in numerical MCQs when scratch work is allowed. It prevents inversion errors.

Practice questions from Balance of payments and exchange rates

Purchasing Power Parity and Interest Rate Parity in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Purchasing Power Parity and Interest Rate Parity: frequently asked questions

What is purchasing power parity in simple words?

It is the idea that a basket of goods should cost the same in every country once prices are converted at the exchange rate. If it does not, the exchange rate tends to move. In the long run, the currency of the higher-inflation country should weaken.

What is the difference between covered and uncovered interest rate parity?

Covered parity uses a forward contract to lock in the future exchange rate, so there is no exchange rate risk. It holds by arbitrage. Uncovered parity uses the expected future spot rate, so it involves risk and often fails in practice.

What is the difference between real and nominal exchange rates?

The nominal exchange rate is the market price of one currency in terms of another. The real exchange rate adjusts it for price levels in both countries. It shows how expensive foreign goods are relative to domestic goods.

Does PPP hold in practice?

Not closely in the short run. Non-traded goods, transport costs, trade barriers and capital flows all cause deviations. It works better as a long-run guide, especially when inflation differences are large.