What is a currency and an exchange rate?
A currency is the money a country (or group of countries) uses: notes, coins and bank balances. India uses the rupee (₹, INR); the USA the dollar ($, USD); many European countries share the euro (€, EUR); Japan uses the yen (¥, JPY).
An exchange rate is the price of one currency in another. If 1 USD = 83 INR, one US dollar costs 83 rupees. The same fact can be written the other way: 1 INR = 1 ÷ 83 ≈ 0.012 USD.
We need exchange rates for travel, buying from other countries (imports), selling to them (exports), studying abroad and sending money home.
How to convert between currencies
Write the rate as 1 A = r B.
- A → B: multiply. Amount in B = amount in A × r.
- B → A: divide. Amount in A = amount in B ÷ r.
Check with sense: if one A is worth many B, you should get more B than A.
For two steps (for example EUR → USD → INR) convert one step at a time, or multiply the two rates. Round money to 2 decimal places only at the end.
Buying rate, selling rate and commission
Banks and money changers quote two rates. They sell you foreign currency at the higher rate and buy it back at the lower rate. The difference is the spread. Some also charge commission: a fixed fee or a percentage.
Example: they sell USD at 84 INR and buy at 82 INR. You buy 100 USD for 8,400 INR, then sell it straight back for 8,200 INR: a loss of 200 INR even though nothing changed.
With a 2% commission on 10,000 INR: fee = 10,000 × 2 ÷ 100 = 200 INR, so only 9,800 INR is converted.
Why rates change: appreciation and depreciation
In most countries the exchange rate floats: it is set by demand and supply in the currency market. More demand for a currency (for example many foreign tourists or buyers of a country's exports) pushes its price up. Interest rates, inflation, trade and confidence all matter. Some countries fix or manage their rate through the central bank.
- Appreciation: a currency buys more foreign currency than before (it gets stronger).
- Depreciation: it buys less (it gets weaker).
If 1 USD goes from 83 to 90 INR, the dollar appreciates and the rupee depreciates. Someone who holds 100 USD now gets 9,000 INR instead of 8,300 INR: a gain of 700 INR. Someone who must pay 100 USD for a laptop now pays 700 INR more: a loss.
Percentage change = (new − old) ÷ old × 100 = 700 ÷ 8,300 × 100 ≈ 8.4%.
Exchange rates and international trade
A strong (appreciating) currency makes imports cheaper and exports dearer for foreigners, so exports may fall. A weak (depreciating) currency makes exports cheaper abroad and imports dearer at home, which can raise prices of imported fuel and parts (inflation).
Memory aid SPICED: Strong Pound (or any currency) Imports Cheap, Exports Dear.
Firms that trade across borders face exchange-rate risk. They can agree a rate in advance (a forward contract) to protect themselves.
Key formulas and definitions
- If 1 A = r B: amount in B = amount in A × r
- Amount in A = amount in B ÷ r
- Inverse rate: 1 B = 1/r A
- Commission = amount × rate % ÷ 100
- Gain or loss = value after − value before
- Percentage change = (new − old) ÷ old × 100
- SPICED: Strong currency → Imports Cheaper, Exports Dearer
Worked examples
1. 1 USD = 83 INR. Convert 45 USD to rupees.
45 × 83 = 3,735 INR.
2. 1 EUR = 90 INR. How many euros do you get for 18,000 INR?
18,000 ÷ 90 = 200 EUR.
3. 1 GBP = 1.25 USD. Write the rate for 1 USD in GBP.
1 USD = 1 ÷ 1.25 = 0.80 GBP.
4. A bank sells USD at 84 INR and buys at 82 INR. Aman buys 250 USD, then sells 50 USD back after his trip. How many rupees did he spend in total?
Buy: 250 × 84 = 21,000 INR. Sell back: 50 × 82 = 4,100 INR. Net spend = 21,000 − 4,100 = 16,900 INR.
5. A changer charges 1.5% commission. You change 20,000 INR into USD at 1 USD = 80 INR. How many dollars do you get?
Fee = 20,000 × 1.5 ÷ 100 = 300 INR. Left = 19,700 INR. 19,700 ÷ 80 = 246.25 USD.
6. An Indian firm will receive 10,000 USD in 3 months. Today 1 USD = 83 INR; when paid, 1 USD = 81 INR. Find the gain or loss in INR and as a percentage.
Expected: 830,000 INR. Received: 810,000 INR. Loss = 20,000 INR. % = 20,000 ÷ 830,000 × 100 ≈ 2.4% loss. The rupee appreciated, which hurt the exporter.
Common mistakes
- Multiplying when you should divide. Write 1 A = r B first and ask: should the answer be bigger or smaller?
- Using the wrong one of the two quoted rates. You pay the bank's selling rate when buying foreign money, and get its buying rate when selling it back.
- Rounding the rate early. Keep all digits and round money to 2 decimal places only at the end.
- Thinking a depreciation is always bad. It hurts importers and travellers but helps exporters and tourism.