Financial Mathematics - Forex Arithmetic | PAPER III – ACCOUNTING & FINANCIAL MANAGEMENT FOR BANKERS | MODULE C: FINANCIAL MANAGEMENT

Financial Mathematics – Forex Arithmetic

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1. Fundamentals of Foreign Exchange

Foreign Exchange (Forex) refers to the mechanism by which the currency of one country is exchanged for that of another. The exchange rate represents the value of one currency in terms of another.

Forex transactions include spot, forward, and swap transactions. Banks and authorized dealers play a central role in facilitating forex trade, which is regulated in India by the RBI under FEMA.

2. Indian Forex Market

The Indian Forex Market is governed by the Reserve Bank of India (RBI) and includes authorized dealers, money changers, and customers. It operates through spot, forward, and derivative instruments.

Key participants include commercial banks, corporates, importers, exporters, and the RBI.

3. Direct and Indirect Quote

• Direct Quote: Amount of domestic currency per unit of foreign currency (e.g., ₹83.20/USD in India).
• Indirect Quote: Amount of foreign currency per unit of domestic currency (e.g., USD 0.0120/₹).

Rule: In Direct Quote, Buy Low and Sell High; in Indirect Quote, Buy High and Sell Low.

4. Basic Exchange Rate Arithmetic

Exchange rate arithmetic involves calculations such as converting foreign currency to domestic currency and vice versa, cross-currency rate determination, and margin application for bid/ask spreads.

Example 1:

USD 1 = ₹83.20 (Direct Quote). Convert USD 500 to INR.

Answer: 500 × 83.20 = ₹41,600

Example 2:

INR 25,000 is to be converted to USD. Rate = ₹83.50/USD (selling rate by bank).

Answer: 25,000 ÷ 83.50 ≈ USD 299.40

Example 3:

If GBP/USD = 1.25 and USD/INR = 83.00, find GBP/INR rate.

Answer: 1.25 × 83.00 = ₹103.75/GBP

Example 4:

Indirect Quote: USD 1 = ₹83.40. Find the indirect quote in USD/INR.

Answer: 1 ÷ 83.40 ≈ USD 0.01199/₹

Example 5:

Forward premium for 3 months is 40 paise. Spot rate = ₹83.20/USD. Find 3-month forward rate.

Answer: 83.20 + 0.40 = ₹83.60/USD

5. Forward Exchange Rates

Forward Exchange Rate is a rate agreed upon today for exchange of currency at a future date. It includes premium or discount based on interest rate differentials between the two currencies.

Forward Rate = Spot Rate ± Forward Premium/Discount.

MCQs – Forex Arithmetic (With Answers)

1. Which of the following is a direct quote in India?

   • a) USD 1 = ₹83.25
   • b) ₹1 = USD 0.012
   • c) USD 1 = GBP 0.80
   • d) GBP 1 = ₹105.00

   Answer: a) USD 1 = ₹83.25

2. In an indirect quote, which principle is followed?

   • a) Buy Low and Sell High
   • b) Buy High and Sell Low
   • c) Always buy at spot rate
   • d) Use fixed exchange rates

   Answer: b) Buy High and Sell Low

3. If USD/INR is 83.20/83.60, what is the spread?

   • a) ₹0.20
   • b) ₹0.40
   • c) ₹0.10
   • d) ₹1.00

   Answer: b) ₹0.40

4. What is the 2-month forward rate if spot rate is ₹83.00/USD and premium is ₹0.30?

   • a) ₹83.00
   • b) ₹83.30
   • c) ₹82.70
   • d) ₹83.60

   Answer: b) ₹83.30

5. If GBP/USD = 1.30 and USD/INR = 83.20, find GBP/INR.

   • a) ₹107.56
   • b) ₹111.00
   • c) ₹108.16
   • d) ₹120.00

   Answer: c) ₹108.16

6. Which institution regulates the forex market in India?

   • a) SEBI
   • b) RBI
   • c) IRDAI
   • d) Ministry of Finance

   Answer: b) RBI

7. If USD 1 = ₹83.40, how many USD will you get for ₹25,000?

   • a) USD 300.00
   • b) USD 350.20
   • c) USD 299.52
   • d) USD 275.60

   Answer: c) USD 299.52

8. When the forward rate is more than the spot rate, the currency is at:

   • a) Discount
   • b) Premium
   • c) Spot
   • d) Arbitrage

   Answer: b) Premium

9. Which of the following is a two-legged forex transaction?

   • a) Forward
   • b) Spot
   • c) Swap
   • d) Cross Rate

   Answer: c) Swap

10. Indirect quote is reciprocal of:

    • a) Cross Rate
    • b) Arbitrage
    • c) Direct Quote
    • d) Forward Rate

    Answer: c) Direct Quote

Additional Cross Currency Forex Arithmetic Examples

6. Example 6: If 1 USD = ₹83.25 and 1 GBP = ₹105.40, what is the cross rate for GBP/USD?
   Solution:
   GBP/USD = ₹105.40 / ₹83.25 = 1.2658
7. Example 7: If 1 EUR = ₹90.50 and 1 JPY = ₹0.57, what is the cross rate for EUR/JPY?
   Solution:
   EUR/JPY = ₹90.50 / ₹0.57 = 158.77
8. Example 8: If 1 AUD = ₹55.30 and 1 CAD = ₹61.20, what is the cross rate for AUD/CAD?
   Solution:
   AUD/CAD = ₹55.30 / ₹61.20 = 0.9039
9. Example 9: If 1 CHF = ₹96.70 and 1 SGD = ₹62.80, find the cross rate for CHF/SGD.
   Solution:
   CHF/SGD = ₹96.70 / ₹62.80 = 1.5408
10. Example 10: If 1 EUR = ₹89.80 and 1 USD = ₹83.60, determine the EUR/USD cross rate.
    Solution:
    EUR/USD = ₹89.80 / ₹83.60 = 1.0743