What an exchange rate is
To buy goods, services or assets from another country, you usually need that country’s money. Currencies are swapped for one another in the foreign exchange market. The price at which one currency is swapped for another is the exchange rate.
Exchange rate: the price of one currency expressed in units of another currency.
An exchange rate is just a price. “A mango costs VD 2” tells you how many valdas one mango costs. “One valda costs 4 kestas” tells you how many kestas one valda costs.
Our fictional currencies:
- Valdoria uses the valda (VD).
- Kestria uses the kesta (KS).
All rates and prices on this page are fictional.
Two ways to quote the same rate
Suppose 1 VD = 4.00 KS. That means 4 kestas buy 1 valda. Dividing both sides by 4:
1 KS = 1 ÷ 4.00 = VD 0.25
These two statements describe the same exchange rate from opposite sides. Each is the reciprocal of the other:
(VD per KS) = 1 ÷ (KS per VD)
Always write the unit as “X per Y” and say which currency is being priced. “The rate is 4” means nothing on its own. “4 KS per VD” is the price of one valda in kestas; “0.25 VD per KS” is the price of one kesta in valdas.
Appreciation and depreciation
- A currency appreciates when it becomes more valuable in terms of another currency: one unit buys more of the other currency.
- A currency depreciates when it becomes less valuable in terms of another currency: one unit buys less of the other currency.
There are only two currencies in an exchange rate, so the changes always come as a pair:
If the valda appreciates against the kesta, the kesta depreciates against the valda, and the other way round.
To decide which currency appreciated, look at the price of that currency:
| Rate change | Price of the valda | Price of the kesta | Result |
|---|---|---|---|
| 1 VD = 4 KS → 1 VD = 5 KS | rises (4 → 5 KS) | falls (0.25 → 0.20 VD) | VD appreciates, KS depreciates |
| 1 VD = 4 KS → 1 VD = 3.2 KS | falls (4 → 3.2 KS) | rises (0.25 → 0.3125 VD) | VD depreciates, KS appreciates |
How currencies are valued relative to one another
In a flexible (floating) exchange rate system, the exchange rate is set by people and firms buying and selling currencies, in the same way that demand and supply set the price of mangoes.
- Who wants valdas? Kestrians who want to buy Valdorian goods and services (Valdorian exports), Kestrian tourists visiting Valdoria, and Kestrian investors who want Valdorian assets such as shares, bonds or bank deposits. To get valdas, they offer kestas.
- Who offers valdas? Valdorians who want Kestrian goods and services (Valdorian imports), Valdorian tourists in Kestria, and Valdorian investors buying Kestrian assets. To get kestas, they offer valdas.
For example, a Kestrian clothing shop orders VD 10,000 of Valdorian fabric when 1 VD = 4 KS. The Valdorian weaver wants to be paid in valdas, so the shop must offer KS 40,000 in the foreign exchange market to buy VD 10,000. In Valdoria’s balance of payments this is an export, a credit. At the same moment, a Valdorian travel agent who books Kestrian hotels for VD 2,000 must sell those valdas to get KS 8,000.
These are exactly the transactions you recorded in the balance of payments in Topic 6.1. Current account and capital and financial account transactions are the reasons people exchange currencies.
When more people want to buy valdas with kestas than want to sell them, the price of the valda in kestas rises: the valda appreciates. When more want to sell valdas than buy them, the valda depreciates. You will draw this market as a graph in Topic 6.3, and study what shifts it in Topic 6.4.
Background. Some governments fix (peg) their exchange rate instead of letting it float, and their central bank buys or sells currency to hold it at the chosen rate. The calculations on this page work the same way for any exchange rate, fixed or flexible.
A month-by-month example
The table shows the fictional valda–kesta rate at the start of each month for half a year, quoted both ways.
| Month | KS per VD (price of 1 VD) | VD per KS (price of 1 KS) |
|---|---|---|
| January | 4.00 | 0.2500 |
| February | 4.20 | 0.2381 |
| March | 4.50 | 0.2222 |
| April | 4.40 | 0.2273 |
| May | 4.80 | 0.2083 |
| June | 5.00 | 0.2000 |
Worked example 1: which currency appreciated, and by how much?
Question. Between January and June the rate moved from 1 VD = 4.00 KS to 1 VD = 5.00 KS. (a) Which currency appreciated? (b) Find the price of the kesta in valdas in each month. (c) Calculate the percentage change in the value of each currency.
(a) One valda now buys 5 kestas instead of 4. The valda buys more kestas, so the valda appreciated and the kesta depreciated.
(b) January: 1 KS = 1 ÷ 4.00 = VD 0.25. June: 1 KS = 1 ÷ 5.00 = VD 0.20. The kesta’s price fell, which confirms (a).
(c) Use the price of each currency in terms of the other.
- Valda: (5.00 − 4.00) ÷ 4.00 × 100 = +25%.
- Kesta: (0.20 − 0.25) ÷ 0.25 × 100 = −20%.
Check. The two changes are not equal in size. Each percentage is measured from a different starting price, so a 25% rise in one currency is a 20% fall in the other. Do not just flip the sign.
Worked example 2: converting prices between currencies
Question. A Valdorian shirt sells for VD 30. A Kestrian laptop sells for KS 2,000. Prices in each home currency do not change. Using the January and June rates, find (a) the price of the shirt in kestas and (b) the price of the laptop in valdas.
Method. Multiply by the rate when converting into the currency on top of the “per”, and divide when converting out of it. A unit check keeps you safe: VD × (KS per VD) = KS.
(a) Shirt. January: 30 VD × 4.00 KS per VD = KS 120. June: 30 × 5.00 = KS 150. For a Kestrian buyer, the shirt is 25% dearer, even though its valda price did not change.
(b) Laptop. January: 2,000 KS ÷ 4.00 KS per VD = VD 500. June: 2,000 ÷ 5.00 = VD 400. For a Valdorian buyer, the laptop is 20% cheaper.
Check. The shirt’s price change for Kestrians (+25%) matches the valda’s appreciation; the laptop’s price change for Valdorians (−20%) matches the kesta’s depreciation. What these price changes do to exports, imports and net exports is the subject of Topic 6.5.
Worked example 3: a small change in the other direction
Question. From March to April the rate moved from 1 VD = 4.50 KS to 1 VD = 4.40 KS. Which currency appreciated, and by what percentage did each currency’s value change?
Which way? One valda now buys fewer kestas (4.40 instead of 4.50), so the valda depreciated and the kesta appreciated.
Valda: (4.40 − 4.50) ÷ 4.50 × 100 = −2.22%.
Kesta: its price rose from 1 ÷ 4.50 = 0.2222 VD to 1 ÷ 4.40 = 0.2273 VD. Divide the new price by the old one without rounding: (1 ÷ 4.40) ÷ (1 ÷ 4.50) = 4.50 ÷ 4.40 = 1.0227, a rise of +2.27%.
Check. For small changes the two percentages are close, but they are still not equal. Keep at least four decimal places when you work with reciprocals, or you may get a noticeably wrong percentage.
Common misconceptions
- “The exchange rate went up, so the currency appreciated.” It depends on how the rate is quoted. A rise in KS per VD is a valda appreciation; a rise in VD per KS is a valda depreciation.
- “Both currencies can appreciate at once.” Against each other, no. If one appreciates, the other depreciates.
- “If the valda rises 25%, the kesta falls 25%.” The kesta falls 20%. Percentages are measured from different bases.
- Multiplying when you should divide. Use units: KS ÷ (KS per VD) = VD.
- “Appreciation means the country’s goods became more expensive at home.” A change in the exchange rate changes the foreign-currency price of a good. Its home-currency price can stay the same, as with the VD 30 shirt.
- “A strong currency is always good.” Appreciation helps a country’s buyers of imports but makes its exports dearer for foreigners. Who gains and who loses is a later topic; do not judge it here.
- “Exchange rates are set by the government.” In a flexible system they are set by buyers and sellers of currencies. Fixed rates are a policy choice some countries make.
Where this leads
Next, Topic 6.3 turns the buying and selling of currencies into a graph: the foreign exchange market, where demand and supply set the equilibrium exchange rate. If the link to international transactions is unclear, revisit Topic 6.1, Balance of Payments Accounts. Try the practice questions now, then use the revision notes and the checklist to consolidate.
Quick questions
Is a 'higher' exchange rate always good for a currency?
Only if you know which way the rate is quoted. A rise in kestas per valda means the valda appreciated; a rise in valdas per kesta means the valda depreciated. Always read the 'per'.
Do I need to draw the foreign exchange market in this topic?
No. Here you define and calculate exchange rates. Drawing the demand and supply graph for a currency is Topic 6.3, and the causes of shifts are Topic 6.4.