Currency and Exchange Rate

Question 1

Based on the exchange rate given above, find the difference between buying and selling price of pound sterling 500.

Solution:

Given information:

• Buying rate: 1 pound sterling = Rs. 150.94
• Selling rate: 1 pound sterling = Rs. 151.65
• Amount: 500 pound sterling

Calculating the buying price:

According to the buying rate, 1 pound sterling = Rs. 150.94

Buying price of 500 pound sterling:

$\text{Buying price} = 500 \times 150.94 = \text{Rs. } 75,470$

Calculating the selling price:

According to the selling rate, 1 pound sterling = Rs. 151.65

Selling price of 500 pound sterling:

$\text{Selling price} = 500 \times 151.65 = \text{Rs. } 75,825$

Finding the difference:

Difference between selling price and buying price:

$\text{Difference} = \text{Rs. } 75,825 - \text{Rs. } 75,470 = \text{Rs. } 355$

Final Answer:

The difference between buying and selling price of 500 pound sterling is Rs. 355.

Verification:

• Buying rate per pound: Rs. 150.94
• Selling rate per pound: Rs. 151.65
• Difference per pound: Rs. 151.65 - Rs. 150.94 = Rs. 0.71
• For 500 pounds: Rs. 0.71 × 500 = Rs. 355 ✓
• This confirms our calculation is correct.

Understanding the concept:

• Buying rate: Rate at which the bank/exchanger buys foreign currency from customers
• Selling rate: Rate at which the bank/exchanger sells foreign currency to customers
• Spread: The difference between selling and buying rates represents the profit margin
• Customer perspective: Always pays more when buying foreign currency, receives less when selling

Note: Currency exchange involves buying and selling rates where banks/exchangers profit from the spread (difference) between these rates. The selling rate is always higher than the buying rate from the customer's perspective.

Question 2

The exchange rate between the American Dollar and Nepali rupees for a specific day is $1 = Rs. 126.35

a) How many American Dollars can be exchanged for Rs. 85,500?
b) How many rupees can be exchanged for $3,000?

Solution:

Given information:

• Exchange rate: $1 = Rs. 126.35

Part (a): Converting Rs. 85,500 to USD

Here, $1 = Rs. 126.35

Or, Rs. 126.35 = $1

Or, Rs. 1 = $\frac{1}{126.35}$

Therefore:

$\text{Rs. } 85,500 = \$ \frac{1}{126.35} \times 85,500 = \$ \frac{85,500}{126.35} = \$676.69$

Part (b): Converting $3,000 to NPR

Again, $1 = Rs. 126.35

Therefore:

$\$3,000 = \text{Rs. } 126.35 \times 3,000 = \text{Rs. } 3,79,050$

Final Answers:

• Part (a): Rs. 85,500 can be exchanged for $676.69
• Part (b): $3,000 can be exchanged for Rs. 3,79,050

Verification:

• Part (a) check: $676.69 × 126.35 = Rs. 85,500.32 ≈ Rs. 85,500 ✓
• Part (b) check: Rs. 3,79,050 ÷ 126.35 = $3,000 ✓

Understanding the conversion process:

• NPR to USD: Divide the NPR amount by the exchange rate (126.35)
• USD to NPR: Multiply the USD amount by the exchange rate (126.35)
• Key formula: Amount in foreign currency = Amount in local currency ÷ Exchange rate
• Reverse formula: Amount in local currency = Amount in foreign currency × Exchange rate

Note: Currency conversion is fundamental in international trade, travel, and finance. The exchange rate represents how much of one currency is needed to purchase one unit of another currency. Always pay attention to which direction the conversion is going.

Question 3

Based on the above mentioned exchange rate, change the following currencies:

a) 1 Canadian Dollar into Japanese Yen
b) 250 Australian Dollar into Swiss Franc

Solution:

Given exchange rates (from previous context):

• 1 Canadian Dollar = Rs. 98.08
• 10 Japanese Yen = Rs. 9.37
• 1 Australian Dollar = Rs. 87.82
• 1 Swiss Franc = Rs. 133.76

Part (a): Converting 1 Canadian Dollar to Japanese Yen

Here, 1 Canadian Dollar = Rs. 98.08

Or, Rs. 98.08 = 1 Canadian Dollar (according to buying rate)

Or, Rs. 1 = $\frac{1}{98.08}$ Canadian Dollar ..................(i)

Again, 10 Japanese Yen = Rs. 9.37

Or, Rs. 9.37 = 10 Japanese Yen (according to the selling rate)

Or, Rs. 1 = $\frac{10}{9.37}$ Japanese Yen ..................(ii)

From equation (i) and (ii), we have:

$\frac{1}{98.08} \text{ Canadian Dollar} = \frac{10}{9.37} \text{ Japanese Yen}$ $1 \text{ Canadian Dollar} = \frac{10 \times 98.08}{9.37} \text{ Japanese Yen} = 104.67 \text{ Japanese Yen}$

Hence, 1 Canadian Dollar = 104.67 Japanese Yen.

Part (b): Converting 250 Australian Dollar to Swiss Franc

1 Australian Dollar = Rs. 87.82

Or, Rs. 87.82 = 1 Australian Dollar

Or, Rs. 1 = $\frac{1}{87.82}$ Australian Dollar ..................(i)

Again, 1 Swiss Franc = Rs. 133.76

Or, Rs. 133.76 = 1 Swiss Franc

Or, Rs. 1 = $\frac{1}{133.76}$ Swiss Franc ..................(ii)

From equation (i) and (ii), we get:

$\frac{1}{87.82} \text{ Australian Dollar} = \frac{1}{133.76} \text{ Swiss Franc}$ $1 \text{ Australian Dollar} = \frac{87.82}{133.76} \text{ Swiss Franc}$ $250 \text{ Australian Dollar} = \frac{87.82}{133.76} \times 250 \text{ Swiss Franc} = 164.14 \text{ Swiss Franc}$

Hence, 250 Australian Dollar = 164.14 Swiss Franc.

Final Answers:

• Part (a): 1 Canadian Dollar = 104.67 Japanese Yen
• Part (b): 250 Australian Dollar = 164.14 Swiss Franc

Verification:

• Part (a): CAD → NPR → JPY: 1 × 98.08 = Rs. 98.08, then Rs. 98.08 ÷ 9.37 × 10 = 104.67 Yen ✓
• Part (b): AUD → NPR → CHF: 250 × 87.82 = Rs. 21,955, then Rs. 21,955 ÷ 133.76 = 164.14 CHF ✓

Understanding cross-currency conversion:

• Method: Convert first currency to common base (NPR), then to target currency
• Formula: Currency A → Currency B = (Currency A to NPR rate) ÷ (Currency B to NPR rate)
• Key insight: NPR acts as the intermediary currency for all conversions
• Real-world application: International business transactions often require cross-currency calculations

Note: Cross-currency conversion involves using a common base currency (here NPR) to convert between two foreign currencies. This method is widely used in international finance when direct exchange rates between two currencies are not readily available.

Question 4

If American Dollar ($) 500 = Pound Sterling (£) 390 and Nepali Rupees Rs. 7,547 = Pound sterling (£) 50, find how many American Dollars can be exchanged for Nepali Rupees 10,308?

Solution:

Given information:

• $500 = £390
• Rs. 7,547 = £50
• Find: How many USD for Rs. 10,308?

Setting up the problem using chain rule:

Let American dollar $x = Nepali Rupees Rs. 10,308

And then write accordingly:

• $500 = £390
• £50 = Rs. 7,547
• Rs. 10,308 = $x

Using chain rule method:

We can set up the chain: USD → GBP → NPR

Using chain rule, we have:

$500 \times 50 \times 10,308 = 390 \times 7,547 \times x$

Solving for x:

$x = \frac{500 \times 50 \times 10,308}{390 \times 7,547}$ $x = \frac{257,700,000}{2,943,330}$ $x = 87.55$

Final Answer:

Hence, $87.55 can be exchanged for Nepali Rupees 10,308.

Verification using step-by-step conversion:

• Step 1: Find NPR to GBP rate: Rs. 7,547 = £50, so Rs. 10,308 = £(50 × 10,308 ÷ 7,547) = £68.25
• Step 2: Find GBP to USD rate: £390 = $500, so £68.25 = $(500 × 68.25 ÷ 390) = $87.50
• Close match: $87.55 ≈ $87.50 (small rounding differences) ✓

Alternative verification using direct rates:

• USD to GBP rate: $500 = £390 → $1 = £0.78
• GBP to NPR rate: £50 = Rs. 7,547 → £1 = Rs. 150.94
• Combined USD to NPR rate: $1 = £0.78 = Rs. (0.78 × 150.94) = Rs. 117.73
• Therefore: Rs. 10,308 = $(10,308 ÷ 117.73) = $87.55 ✓

Understanding the chain rule method:

• Principle: Set up equivalent ratios in a chain format
• Method: Multiply all numerators and set equal to product of all denominators
• Key insight: The unknown appears in one term, making it solvable
• Advantage: Handles multiple currency conversions in one equation

Note: The chain rule method is particularly useful for multi-step currency conversions where you need to find an unknown amount through intermediate currencies. This method ensures mathematical consistency across all exchange rate relationships.

Question 5

A businessman exchanged Nepali Rupees 8,40,000 at the exchange rate of the Pound Sterling (£) 1 = Rs. 150. After 5 days, Nepali currency is deflated by 5% and then he exchanged Nepali currency into Pound Sterling. How much profit or loss does he get?

Solution:

Given information:

• Initial amount: Rs. 8,40,000
• Initial exchange rate: £1 = Rs. 150
• Rate of deflation: 5%
• Time period: 5 days

Step 1: Initial conversion from NPR to GBP

A businessman exchanged the Pound Sterling for Rs. 8,40,000

Now, Rs. 150 = £1

Or, Rs. 1 = £$\frac{1}{150}$

Therefore:

$\text{Rs. } 8,40,000 = £\frac{1}{150} \times 8,40,000 = £\frac{8,40,000}{150} = £5,600$

Step 2: Currency deflation effect

Since Nepali currency is deflated by 5% in 5 days, then new exchange rate is:

$£1 = \text{Rs. } (150 - 5\% \text{ of } 150) = 150 - 150 \times \frac{5}{100} = \text{Rs. } 150 - \text{Rs. } 7.50 = \text{Rs. } 142.50$

Step 3: Converting back from GBP to NPR

Again, he exchanged his Pound Sterling into Nepali Rupee.

Thus:

$£5,600 = \text{Rs. } 142.50 \times 5,600 = \text{Rs. } 7,98,000$

Step 4: Calculating profit or loss

Initial amount: Rs. 8,40,000

Final amount: Rs. 7,98,000

Here, Rs. 7,98,000 < Rs. 8,40,000 so he gets a loss.

Hence, loss amount = Rs. 8,40,000 - Rs. 7,98,000 = Rs. 42,000

Final Answer:

The businessman incurs a loss of Rs. 42,000.

Verification and analysis:

• Initial conversion: Rs. 8,40,000 → £5,600 at rate £1 = Rs. 150
• Currency deflation: NPR weakens by 5%, new rate £1 = Rs. 142.50
• Final conversion: £5,600 → Rs. 7,98,000 at new rate
• Loss percentage: (42,000/8,40,000) × 100% = 5%
• Key insight: The loss percentage equals the deflation percentage

Understanding currency deflation impact:

• Deflation: When a currency loses value relative to other currencies
• Effect on exchange: You get fewer foreign currency units for the same local currency amount
• Risk for traders: Currency fluctuations can lead to significant gains or losses
• Timing importance: The timing of currency exchange matters in volatile markets

Note: This problem demonstrates how currency deflation affects foreign exchange transactions. When the local currency (NPR) deflates against a foreign currency (GBP), anyone holding the local currency and then converting back suffers a loss proportional to the deflation rate.

Question 6

A businessman of Nepali origin from Norway purchased 900 Pasmina shawls at the rate of Rs. 4,000 in Kathmandu. He exported by paying 5% export tax and then at how much Euro should he sell all the shawls at the profit of 20%? (€1 = Rs. 130)

Solution:

Given information:

• Number of Pasmina shawls: 900
• Price per shawl: Rs. 4,000
• Export tax: 5%
• Desired profit: 20%
• Exchange rate: €1 = Rs. 130

Step 1: Calculate the initial cost

Here, the price of a Pasmina shawl = Rs. 4,000

The cost of 900 shawls:

$\text{Cost} = \text{Rs. } 4,000 \times 900 = \text{Rs. } 36,00,000$

Step 2: Calculate cost including export tax

The cost price of the shawls including 5% export tax:

$\text{Total cost} = \text{Rs. } 36,00,000 + 5\% \text{ of Rs. } 36,00,000$ $= \text{Rs. } 36,00,000 + \text{Rs. } 36,00,000 \times \frac{5}{100}$ $= \text{Rs. } 36,00,000 + \text{Rs. } 1,80,000$ $= \text{Rs. } 37,80,000$

Step 3: Convert total cost to Euros

We know that, €1 = Rs. 130

Or, Rs. 130 = €1

Or, Rs. 1 = €$\frac{1}{130}$

Therefore:

$\text{Rs. } 37,80,000 = €\frac{1}{130} \times 37,80,000 = €29,076.92$

∴ The total cost price in euro = €29,076.92

Step 4: Calculate selling price for 20% profit

To sell at the profit of 20%:

$\text{Selling price} = \text{Cost price} + 20\% \text{ of cost price}$ $\text{Selling price} = €29,076.92 + €29,076.92 \times \frac{20}{100}$ $= €29,076.92 + €5,815.38$ $= €34,892.30$

Final Answer:

Hence, the selling price of all the shawls should be €34,892.30.

Verification and breakdown:

• Initial cost: 900 × Rs. 4,000 = Rs. 36,00,000
• Export tax (5%): Rs. 36,00,000 × 0.05 = Rs. 1,80,000
• Total cost in NPR: Rs. 36,00,000 + Rs. 1,80,000 = Rs. 37,80,000
• Total cost in EUR: Rs. 37,80,000 ÷ 130 = €29,076.92
• Profit (20%): €29,076.92 × 0.20 = €5,815.38
• Selling price: €29,076.92 + €5,815.38 = €34,892.30

Alternative calculation check:

• Cost per shawl including tax: Rs. 37,80,000 ÷ 900 = Rs. 4,200
• Cost per shawl in EUR: Rs. 4,200 ÷ 130 = €32.31
• Selling price per shawl: €32.31 × 1.20 = €38.77
• Total selling price: €38.77 × 900 = €34,893 ≈ €34,892.30 ✓

Understanding international trade costs:

• Base cost: The initial purchase price of goods
• Export tax: Government levy on goods leaving the country
• Currency conversion: Exchange rate impact on international transactions
• Profit margin: Markup percentage for business sustainability

Note: This problem demonstrates the complexity of international trade calculations, involving multiple cost components (base price, taxes) and currency conversions. Export taxes increase the cost base, which affects the final selling price needed to achieve the desired profit margin.