Currency and Exchange Rate

Wherever we travel or trade, we pay in the money of that country, and money sent home from any country reaches the family as Nepali rupees. A country’s money is its currency: the Nepali rupee (Rs), the US dollar ($), the Indian rupee (₹), the Qatari riyal. Changing one currency for another is money exchange (in Nepali, सटही).

The price of one currency in another is the exchange rate (for another country’s money, the foreign exchange rate). In Nepal, Nepal Rastra Bank decides it. It fixes the rate for the Indian rupee: ₹100 = Rs 160, the same every day for over thirty years. The rates of the other currencies change with the world’s markets, and Nepal Rastra Bank publishes them each morning; banks and money changers may quote rates a little different from its own.

Every rate is given twice, and both are from the bank’s side of the counter:

• the buying rate is what the bank pays when it buys foreign money from you: you bring dollars, you get rupees;
• the selling rate is what the bank charges when it sells foreign money to you: you bring rupees, you get dollars.

So a family receiving dollars from abroad is paid at the buying rate, and a student going to study in America buys dollars at the selling rate. Either way the bank does better than you would on a rate halfway between: that is fair, since it does the work, but it means changing money and changing it straight back always loses a little.

Try a round trip yourself: change rupees into a currency and straight back, and see what the two rates cost you.

Every change of money is one of two moves: foreign money into rupees (the bank buys), or rupees into foreign money (the bank sells).

$$\text{rupees} = \text{foreign money} \times \text{buying rate}$$
$$\text{foreign money} = \frac{\text{rupees}}{\text{selling rate}}$$

When a question gives a single rate (“$1 = Rs 126.35”), use that one for both. Round rupees and foreign money to two decimal places at the end.

Banks in Nepal deal in rupees. To change Canadian dollars into Japanese yen at a bank here, you sell the Canadian dollars for rupees (at the buying rate), then buy yen with those rupees (at the selling rate). There are two ways to set out the working.

The chain rule

The second way is a shortcut for the same thing, the chain rule. Write a chain of equal amounts, each line starting with the currency the line before ended with, until the chain comes back to where it started. Then the product of the left-hand numbers equals the product of the right-hand numbers.

Why does it work? Each line says “these two amounts are worth the same”, so its two sides could be swapped for each other. Multiply the three left-hand amounts and the three right-hand ones: every currency appears once on each side, so the units cancel and what is left is an equation in numbers. For Example 3a:

$$\begin{aligned} 1 \times 10 \times 98.08 &= x \times 9.37 \times 1 \\ x &= \frac{10 \times 98.08}{9.37} = 104.67 \end{aligned}$$

the same ¥104.67. For 3b: AUD 250 = CHF x; CHF 1 = Rs 133.76; Rs 87.82 = AUD 1, so 250 × 1 × 87.82 = x × 133.76 × 1 and x = 164.14.

In general: if a of one currency = b of a second, c of the second = d of a third, and e of the third = f of the first, then a × c × e = b × d × f. The chain may have as many links as needed.

Rates change. When a dollar costs more rupees than before, the rupee has lost value against it: the rupee has been devalued (अवमूल्यन). When a dollar costs fewer rupees, the rupee has gained value: it has been revalued (अधिमूल्यन). Newspapers say the rupee has weakened or strengthened.

Exam questions give the change as a percentage of the rate. If the rupee is devalued by R%, a dollar costs R% more rupees:

$$\text{new rate} = \text{old rate} \times \left(1 + \frac{R}{100}\right)$$

If the rupee is revalued by R%, a dollar costs R% fewer rupees:

$$\text{new rate} = \text{old rate} \times \left(1 - \frac{R}{100}\right)$$

This is Unit 3’s growth and depreciation, applied to the price of a dollar. If $1 = Rs 150 and the rupee is devalued by 10%, then $1 = 150 × 1.1 = Rs 165.

Back to the opening

When the rupee loses value, whoever is paid in foreign money and spends in rupees gains; whoever earns rupees and pays in foreign money loses.

The family receiving $500 gains: the same dollars buy more rupees. The student paying fees abroad loses, and so does anyone buying goods from outside India: a phone, a laptop, fuel, a plane ticket priced in dollars cost more rupees. So part of the family’s gain is eaten up by higher prices in the shops. And because the Indian rupee’s rate is fixed, everything Nepal buys from India costs the same in rupees as before, however the dollar moves.

Real trade mixes this unit with profit and loss, taxes and Unit 3’s percentages. Work in one currency all the way, then change once at the end (or change first, then work).

In the SEE’s Compulsory Mathematics paper, Arithmetic carries 13 marks in three questions (compound interest; growth and depreciation; currency and exchange), with knowledge, understanding, application and higher-ability parts spread among them (CDC’s specification grid). In CDC’s model paper the currency question looks like this:

Part	Level	Marks	What it asks
a.	application	2	rupees into a foreign currency at the right rate
b.	application	1	the foreign money changed back
c.	higher ability	1	the profit or loss, with the reason

Here is a question in that shape, and a longer one to practice with.

Question 1

Question 2

Using the buying rates in the table of Activity 1, change these into Nepali rupees.

Question 3

Using the selling rates in the table, change Rs 2,00,000 into these currencies.

Question 4

On a certain day Nepal Rastra Bank’s buying and selling rates for $1 are Rs 127.50 and Rs 128.

Question 5

On 23 August 2022 Nepal Rastra Bank’s buying and selling rates for 1 Chinese yuan were Rs 18.64 and Rs 18.73.

Question 6

Using the rates in the table of Activity 1, answer these.

Question 7

Sobita went from Nepal to Australia for higher studies. Now she works there as a secondary-school teacher, earning 37 Australian dollars an hour. She teaches 5 hours a day, every day except Saturday. Take AUD 1 = Rs 90.

Question 8

Question 9

Question 10

Question 11

Question to discuss

These questions mix Unit 2 (compound interest), Unit 3 (growth and depreciation) and this unit, as the SEE’s Arithmetic questions do.

Question 1

A family wants to deposit Rs 4,00,000 in the name of their child, 17 years old and just starting Grade 11, for the child’s studies. The money, with interest, will be taken out when the child has passed Grade 12, at 19. A development bank offers three choices: first, 19% a year compound interest, compounded yearly; second, 18% a year compounded half-yearly; third, 20% a year simple interest.

Question 2

A sum of money grows to Rs 12,000 in 2 years and to Rs 13,200 in 3 years at compound interest, compounded yearly.

Question 3

A man bought land for Rs 80,00,000 on Baisakh 25, 2075 BS and began building a house on it the same day; the house cost Rs 2,70,00,000. The land’s price rises by 20% a year, and the house’s value falls by 20% a year.

Question 4

Ram changed some Nepali rupees into US dollars at $1 = Rs 110. Five days later the Nepali rupee was devalued by 10% against the dollar, and by changing the same dollars back into rupees he made a profit of Rs 33,000.

Question 5

Nepal Bank Limited’s management committee decided on these rates for fixed deposits, compounded half-yearly:

Deposit period	Rate of interest (a year)	Least deposit
up to 6 months	6.75%	Rs 50,000
6 months to 1 year	7.25%	Rs 50,000
1 year to 6 years	7.5%	Rs 75,000

Sujit Thakur borrowed Rs 2,00,000 from a cooperative, to be paid back in 2 years at 5% a year simple interest. At once he put the same sum in a fixed deposit at Nepal Bank for the same 2 years.

Question 6

Anish came home from 5 years’ work in the United Arab Emirates with AED 60,000, and changed it all into rupees at AED 1 = Rs 34.83. He put the money in a fixed deposit at Nepal Bank for 1 year, with interest compounded half-yearly at these rates:

Deposit period	Rate of interest (a year)	Least deposit
up to 6 months	9%	Rs 50,000
6 months to 1 year	10%	Rs 50,000
1 year to 5 years	12%	Rs 75,000

Question 7

At the end of 2020 AD a 4-aana plot of land in Kathmandu was priced at Rs 60,00,000. At the start of 2021 its price rose by 10% as many people wanted to buy land, but at the end of 2022 it fell by 4% in an economic slowdown.

Question 8

To go abroad for work, Kul Bahadur borrowed Rs 2,50,000 from a cooperative for 2 years at 15% a year, compounded yearly. After 1 year he sent home MYR 7,000 from his savings; his wife changed it at MYR 1 = Rs 28.58 and paid it off the loan. She will pay the rest, with interest at the same rate, a year later.

Question 9

A person borrowed Rs 1,50,000 for 2 years at 10% a year, compounded yearly, and paid back Rs 85,000 at the end of the first year.