
Forex Arithmetic: Cross Rates, Forward Points & Swaps
BFM Paper 2 (BFM Module A — Exchange Rates, Forex Arithmetic, FEDAI Rules & Documentary Credits) — 3 Solved Case Sets & Interactive Calculator
Conquer the most feared numerical module in CAIIB BFM Module A: Chain Rule Cross Rates (Bid × Bid for Buying, Ask × Ask for Selling), Ascending vs Descending Forward Points, Deducting vs Adding Exchange Margin ("Buy Low, Sell High"), Transit Period interest on Export Sight Bills, and Early/Late Forward Delivery under FEDAI Rules.
Core Formulas, RBI Benchmarks & Examiner Traps
| Concept / Metric | Exact Mathematical Formula | RBI Regulatory Norm / Benchmark | Common IIBF Examiner Trap |
|---|---|---|---|
| Golden Rule of Merchant Rates (Buy Low, Sell High) | Buying Rate = Interbank Bid Rate × (1 - Exchange Margin%); Selling Rate = Interbank Ask Rate × (1 + Exchange Margin%) | Under Direct Quotation (₹ per 1 unit of Foreign Currency), bank buys foreign currency at the lower rate and sells at the higher rate. | Always DEDUCT Exchange Margin for Buying Rates (TT Buying / Bill Buying) and ADD Exchange Margin for Selling Rates (TT Selling / Bill Selling)! |
| Forward Points (Premium vs Discount Rule) | If Forward Points are Low / High (Ascending, e.g., 20/25 paise) -> Foreign Currency is at PREMIUM (ADD to Spot). If High / Low (Descending, e.g., 30/20 paise) -> Foreign Currency is at DISCOUNT (DEDUCT from Spot). | For Export Customer Buying Rate at Premium: take Premium up to the START of the delivery month (worst case for customer / best for bank). For Import Selling Rate at Premium: take Premium up to the END of the delivery month. | Never pass on future forward premium to an exporter before the customer actually delivers the foreign currency! |
| Cross Rate Multiplication vs Division | (EUR/INR)_Bid = (EUR/USD)_Bid × (USD/INR)_Bid | (EUR/INR)_Ask = (EUR/USD)_Ask × (USD/INR)_Ask | When dividing (e.g., USD/JPY given to find JPY/INR = (USD/INR) / (USD/JPY)): Bid = (USD/INR)_Bid / (USD/JPY)_Ask (Cross-division!) | Multiplication is straight (Bid × Bid, Ask × Ask), whereas Division is cross (Bid / Ask for Buying, Ask / Bid for Selling)! |
EUR/INR Cross Rate, Export Bill Buying Rate & Forward Premium Calculation
An Indian exporter presents a Sight Export Bill for EUR 1,00,000 drawn on a German buyer. The interbank foreign exchange market quotes are as follows: Spot USD/INR = 83.40 / 83.50; 1-Month Forward = 15 / 20 paise; 2-Month Forward = 32 / 38 paise; 3-Month Forward = 50 / 58 paise. Spot EUR/USD = 1.0820 / 1.0840. Exchange Margin for TT Buying is 0.10% and for Bill Buying is 0.15%. Normal transit period for sight bills is 25 days (approximate as 1-month forward or ignore forward premium if sight spot).
| Market Parameter | Bid / Ask Quote |
|---|---|
| Interbank Spot USD/INR | 83.40 / 83.50 |
| USD/INR Forward Points (1M | 2M | 3M) | 15/20 p | 32/38 p | 50/58 p |
| Interbank Spot EUR/USD | 1.0820 / 1.0840 |
| Exchange Margin (TT Buying | Bill Buying | TT Selling) | 0.10% | 0.15% | 0.15% |
What is the Interbank Spot EUR/INR Bid (Buying) and Ask (Selling) Cross Rate (rounded to 4 decimal places)?
(EUR/INR)_Bid = (EUR/USD)_Bid × (USD/INR)_Bid; (EUR/INR)_Ask = (EUR/USD)_Ask × (USD/INR)_Ask- Step 1: To buy EUR against INR, bank sells EUR for USD at EUR/USD Bid (1.0820) and sells USD for INR at USD/INR Bid (83.40): 1.0820 × 83.40 = ₹90.2388.
- Step 2: To sell EUR against INR, bank buys EUR with USD at EUR/USD Ask (1.0840) and buys USD with INR at USD/INR Ask (83.50): 1.0840 × 83.50 = ₹90.5140.
If an exporter receives an inward telegraphic remittance (TT) of EUR 1,00,000 today, what is the Merchant Spot TT Buying Rate (after 0.10% Exchange Margin, rounded to 4 decimals) and the INR amount credited?
TT Buying Rate = Interbank Spot Bid × (1 - Exchange Margin %)- Step 1: Interbank Spot EUR/INR Bid = ₹90.2388.
- Step 2: Less 0.10% Exchange Margin = 90.2388 × (1 - 0.0010) = 90.2388 - 0.0902 = ₹90.1486.
- Step 3: INR Credited for EUR 1,00,000 = 1,00,000 × 90.1486 = ₹90,14,860.
An exporter presents a 2-Month Usance Export Bill in USD (where 2-Month Forward premium is 32/38 paise and transit period adds 1 month, making total realization 3 months = 50/58 paise). What is the Interbank 3-Month Forward USD/INR Buying Rate before margin?
3M Interbank Forward Bid = Spot Bid + 3M Forward Bid Premium- Step 1: Spot USD/INR Bid = ₹83.40.
- Step 2: Forward points (50/58 paise) are ascending (Low/High), so USD is at a Premium.
- Step 3: Add 3M Bid Premium (₹0.50) to Spot Bid = 83.40 + 0.50 = ₹83.90.
Using the 3M Interbank Forward USD/INR Buying Rate of ₹83.90 and a Bill Buying Margin of 0.15%, what is the Bill Buying Rate quoted to the USD exporter (rounded to 4 decimals)?
Bill Buying Rate = Interbank Forward Bid × (1 - Bill Buying Margin %)- Step 1: Interbank Forward Bid = ₹83.9000.
- Step 2: Less 0.15% Bill Buying Margin = 83.90 × 0.0015 = ₹0.12585.
- Step 3: Merchant Bill Buying Rate = 83.9000 - 0.12585 = ₹83.77415 (rounded to ₹83.7742 or ₹83.7750 per 0.0025 multiple).
An importer requests a 2-Month Forward Import Contract for USD 50,000 (delivery at any time during the 2nd month). Using Spot Ask ₹83.50, 1M Forward 15/20p, 2M Forward 32/38p, and 0.15% Selling Margin, what rate will the bank quote?
Forward Import Selling Rate (at Premium) = (Spot Ask + Full 2M Ask Premium) × (1 + Selling Margin %)- Step 1: Since USD is at a premium and this is a Selling Contract, the bank charges the maximum premium up to the end of the 2nd month (38 paise = ₹0.38).
- Step 2: Interbank 2M Forward Ask = 83.50 + 0.38 = ₹83.8800.
- Step 3: Add 0.15% Selling Margin = 83.8800 × (1 + 0.0015) = 83.8800 + 0.12582 = ₹84.0058.
Cross-Division (JPY/INR Rate) & Forward Points at a Discount
An Indian auto firm imports precision robotics from Tokyo invoiced in Japanese Yen (JPY 5,00,00,000 — 50 Million Yen). The market quotes are: Spot USD/INR = 83.50 / 83.60; Spot USD/JPY = 154.20 / 154.50. Suppose 3-Month Forward USD/JPY points are 180 / 160 sen (1 Yen = 100 sen). Exchange Margin for TT Selling is 0.15% and for Bill Selling is 0.20%.
| Currency Pair | Spot Quote | 3M Forward Points |
|---|---|---|
| USD / INR | 83.50 / 83.60 | 40 / 48 paise (Ascending = Premium) |
| USD / JPY | 154.20 / 154.50 | 180 / 160 sen = 1.80 / 1.60 Yen (Descending = Discount) |
As per FEDAI rules, Japanese Yen (JPY) against INR is always quoted in units of how many Yen, and how do we compute the Interbank Spot JPY/INR Ask (Selling) Rate?
Spot (100 JPY/INR)_Ask = [(USD/INR)_Ask / (USD/JPY)_Bid] × 100- Step 1: Per FEDAI Rule, JPY, IDR, and Kenyan Shilling are quoted per 100 units of foreign currency.
- Step 2: To sell JPY to the customer against INR, the bank buys USD against INR at USD/INR Ask (83.60) and sells that USD to buy JPY at USD/JPY Bid (154.20).
- Step 3: Therefore, cross-division applies: (USD/INR Ask ÷ USD/JPY Bid) × 100.
Calculate the Interbank Spot (100 JPY / INR) Bid and Ask rates (to 4 decimal places).
Bid = (83.50 / 154.50) × 100; Ask = (83.60 / 154.20) × 100- Step 1: Interbank Spot Bid (per 100 JPY) = (83.50 / 154.50) × 100 = ₹54.0453.
- Step 2: Interbank Spot Ask (per 100 JPY) = (83.60 / 154.20) × 100 = ₹54.2153.
What is the Spot Bill Selling Rate (with 0.20% total margin) for the import bill of JPY 5,00,00,000, and what is the INR amount payable by the importer?
Bill Selling Rate = Interbank Spot Ask × (1 + Bill Selling Margin %)- Step 1: Interbank Spot Ask per 100 JPY = ₹54.2153.
- Step 2: Add 0.20% Bill Selling Margin = 54.2153 × 1.0020 = ₹54.3237 per 100 JPY.
- Step 3: Total INR Payable for 5,00,000 units of (100 JPY) = 5,00,000 × 54.3237 = ₹2,71,61,850.
Examine the 3-Month Forward USD/JPY points (1.80 / 1.60 Yen). Since the points are High / Low (Descending), what is the 3-Month Outright Interbank Forward USD/JPY Bid and Ask quote?
When Forward Points are High / Low (Discount): Subtract from Spot (Spot Bid - High Discount / Spot Ask - Low Discount)- Step 1: Descending points (1.80 / 1.60) mean USD is at a Discount against JPY (because Japanese interest rates are lower than US interest rates).
- Step 2: 3M Forward USD/JPY Bid = 154.20 - 1.80 = 152.40.
- Step 3: 3M Forward USD/JPY Ask = 154.50 - 1.60 = 152.90.
Using 3M Forward USD/INR Ask (83.60 + 0.48 = 84.08) and 3M Forward USD/JPY Bid (152.40), what is the 3M Interbank Forward Ask rate per 100 JPY?
3M Forward (100 JPY/INR)_Ask = (3M Forward USD/INR Ask ÷ 3M Forward USD/JPY Bid) × 100- Step 1: 3M Forward USD/INR Ask = 83.60 + 0.48 = 84.08.
- Step 2: 3M Forward USD/JPY Bid = 152.40.
- Step 3: 3M Forward (100 JPY/INR) Ask = (84.08 / 152.40) × 100 = ₹55.1706 per 100 JPY.
Cancellation & Early Delivery of Forward Contracts (FEDAI Rule 6)
An exporter booked a 3-Month Forward Sale Contract with your bank for USD 2,00,000 at a contracted rate of ₹84.10 per USD. On the due date, the exporter fails to deliver the export proceeds and requests cancellation of the contract. On the date of cancellation, the Interbank Spot USD/INR quote is 84.50 / 84.60. The bank’s Exchange Margin is 0.10% for TT Buying and 0.15% for TT Selling.
| Contract & Market Detail | Rate / Amount |
|---|---|
| Original Contracted Forward Purchase Rate (Bank Buying USD) | ₹84.1000 per USD |
| Contracted Amount | USD 2,00,000 |
| Spot USD/INR on Date of Cancellation | 84.50 / 84.60 |
| Exchange Margin (TT Buying | TT Selling) | 0.10% | 0.15% |
Under FEDAI Rule 6, when a customer cancels an Export Forward Sale Contract (which was a Forward Purchase Contract for the bank), at what rate must the bank cancel the contract?
Purchase Contract is cancelled at Opposite TT Selling Rate; Sale Contract is cancelled at Opposite TT Buying Rate- Step 1: Originally, the bank contracted to BUY USD 2,00,000 from the exporter at ₹84.10.
- Step 2: To close out/cancel a Purchase Contract when the customer fails to deliver, the bank must SELL back (or buy from market at Ask + margin) using the opposite rate: Spot TT Selling Rate.
Calculate the Spot TT Selling Rate on the date of cancellation (rounded to 4 decimal places).
TT Selling Rate = Interbank Spot Ask × (1 + TT Selling Margin %)- Step 1: Interbank Spot Ask on cancellation date = ₹84.6000.
- Step 2: Add 0.15% TT Selling Margin = 84.60 × 1.0015 = ₹84.7269.
What is the Exchange Difference per USD and the total Cancellation Charge recovered from (or paid to) the exporter on USD 2,00,000?
Cancellation Charge = (TT Selling Rate - Contracted Purchase Rate) × Contract Amount- Step 1: Bank contracted to buy USD at ₹84.1000, but now has to buy/cover at TT Selling Rate ₹84.7269.
- Step 2: Loss per USD = 84.7269 - 84.1000 = ₹0.6269 per USD.
- Step 3: Total Cancellation Loss recovered from exporter = 2,00,000 × 0.6269 = ₹1,25,380 (plus flat FEDAI cancellation handling fee).
Suppose instead of cancelling, the exporter delivered USD 2,00,000 one month EARLY. Under FEDAI rules, at what rate is the early delivery settled initially, and what other adjustments apply?
Early Delivery Settlement = Contracted Rate ± Swap Cost/Gain ± Interest on Outlay/Inflow of Funds- Step 1: On early delivery, the bank always gives the customer the original contracted rate (₹84.10) first.
- Step 2: Because the bank had sold USD 1-month forward in the interbank market to cover the original maturity, the bank must execute a Buy/Sell or Sell/Buy Swap for 1 month and recover/pass on the Swap Difference.
- Step 3: Furthermore, if the interbank spot rate differs from the contracted rate, there is an Outlay or Inflow of INR funds for 1 month, on which interest is charged/paid.
In an early delivery of an Export Purchase Contract (Contracted Rate = ₹84.10) where the bank covers in the interbank market at Spot ₹84.50, is there an Outlay of Funds or Inflow of Funds for the bank during the early 1-month period?
Cash Flow = Interbank Spot Sale Receipt (₹84.50) - Customer Payment at Contracted Rate (₹84.10)- Step 1: Bank pays the exporter at the contracted rate = ₹84.10 per USD.
- Step 2: Bank sells the delivered USD in the interbank spot market (as part of the Sell Spot / Buy Forward swap) and receives ₹84.50 per USD.
- Step 3: Net Surplus (Inflow of Funds) with the bank for 1 month = 84.50 - 84.10 = +₹0.40 per USD × 2,00,000 = ₹80,000.
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Frequently Asked IIBF Exam Questions (BFM Paper 2)
When are exchange gains NOT passed on to the customer upon cancellation of a forward contract?
Under FEDAI Rule 6, if a forward contract is cancelled at the customer’s request ON or BEFORE the maturity date, any exchange gain is passed to the customer. However, if the contract becomes OVERDUE and is cancelled after the maturity date, the customer must pay any exchange loss, while any exchange gain is retained by the bank (unless delay was beyond customer control and accepted by the bank).
What is the difference between TT Buying Rate and Bill Buying Rate?
TT Buying Rate applies when the bank’s Nostro account is already credited with foreign currency (or there is no realization delay). Bill Buying Rate applies when the bank purchases/discounts an export bill where foreign currency will be realized only on a future date (after transit + usance period), so forward points and a slightly higher bill margin are applied.

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