Exam practice

Changing the money (currency) of one country for that of another, at an exchange rate: for example Nepali rupees for US dollars at a bank.

The selling rate: the bank is selling dollars to the student.

The buying rate is the rate at which a bank or financial institution buys foreign currency from customers (pays rupees for it). The selling rate is the rate at which it sells foreign currency to customers (takes rupees for it). The selling rate is the higher.

$1425 \times \frac{160}{100} =$ Rs 2,280.

2000 × 127.35 = Rs 2,54,700.

4672 × 150.94 = Rs 7,05,191.68.

672 × 87.82 = Rs 59,015.04.

1851 × 33.91 = Rs 62,767.41.

2225 × 34.82 = Rs 77,474.50.

$58230 \times \frac{9.58}{100} = 5578.43$: Rs 5,578.43.

4512 × 16.23 = Rs 73,229.76.

6725 × 28.45 = Rs 1,91,326.25.

3450 × 18.70 = Rs 64,515.

$\frac{200000}{88.23} = 2266.80$: AUD 2,266.80.

$\frac{200000}{127.95} = 1563.11$: $1,563.11.

$\frac{200000}{128.73} = 1553.64$: €1,553.64.

$\frac{200000}{34.83} = 5742.18$: AED 5,742.18.

The bank sells dollars: $\frac{81280}{128} =$ $635.

The bank buys dollars: 600 × 127.50 = Rs 76,500.

$\frac{37460}{18.73} =$ CNY 2,000.

5000 × 18.64 = Rs 93,200.

The bank buys the euro for Rs 128.13 and sells dirhams at Rs 34.83: $\frac{128.13}{34.83} = 3.68$. €1 = AED 3.68.

$\frac{34.82}{28.58} = 1.22$. QAR 1 = MYR 1.22.

The bank buys the US dollars: 200 × 127.35 = Rs 25,470. It sells Canadian dollars at Rs 98.54: $\frac{25470}{98.54} = 258.47$. $200 = CAD 258.47.

$\frac{200 \times 150.94}{3.59} = \frac{30188}{3.59} = 8408.91$. £200 = ฿8,408.91.

A week: 6 × 5 = 30 hours; 30 × 37 = 1110 Australian dollars.
1110 × 90 = Rs 99,900.

30 − 4 = 26 working days; 26 × 5 × 37 = 4810 Australian dollars.
4810 × 90 = Rs 4,32,900.

Dollars: $\frac{1240000}{124} = 10000$.
New rate: 124 × 1.1 = 136.40. Back: 10000 × 136.40 = 1364000.
A profit of Rs 1,24,000.

Baht: $\frac{720000}{3.60} = 200000$.
New rate: 3.60 × 0.95 = 3.42. Back: 200000 × 3.42 = 684000.
A loss of Rs 36,000.

Price: 10000 × 34.50 = 345000.
With 20% duty: 345000 × 1.2 = 414000. With 13% VAT: 414000 × 1.13 = 467820.
Rs 4,67,820.

Cost price: $\frac{21600}{1.2} =$ ₹18,000. For 25% profit: 18000 × 1.25 = ₹22,500.
In rupees: 22500 × 1.6 = Rs 36,000.

Shawls with tax: 500 × 3500 × 1.05 = 1837500. Transport: 30 × 88.50 = 2655.
Cost price: 1837500 + 2655 = 1840155.
Selling price: 500 × 80 × 88.50 = 3540000.
Profit: 3540000 − 1840155 = 1699845; $\frac{1699845}{1840155} \times 100\% = 92.38\%$.
A profit of 92.38%.

From Thailand: 8600 × 3.50 = Rs 30,100. Kathmandu is cheaper by 30100 − 28000 = 2100.
$\frac{2100}{30100} \times 100\% = 6.98\%$. It is 6.98% cheaper bought in Kathmandu.

Chain: Rs x = $132; $176 = £100; £1 = Rs 151.
x × 176 × 1 = 132 × 100 × 151, so $x = \frac{1993200}{176} =$ Rs 11,325.

₹7,500 = 75 × 160 = Rs 12,000; $\frac{12000}{120} =$ $100.

5612 × 18.70 = Rs 1,04,944.40; $\frac{104944.40}{33.91} = 3094.79$. SAR 3,094.79.

A bank buys foreign currency for less than it sells it for. The difference pays for its costs (staff, counting and keeping cash, sending money abroad) and for the risk that the rate moves while it holds the currency, and leaves a profit. Where the risk is small, as with the Indian rupee’s fixed rate, the gap is small too.

Twice a year for 2 years: 4 times.

First: $400000 \times 1.19^2 = 566440$.
Second: $400000 \times 1.09^4 = 564632.64$.
Third: $400000 + 400000 \times \frac{20 \times 2}{100} = 560000$.
The first choice gives the most, Rs 5,66,440. (No Nepali bank pays such rates on deposits today: the best in July 2026 was about 4.55% a year. The comparison is the point.)

$\text{CI} = P\left[\left(1 + \frac{R}{100}\right)^T - 1\right]$

The third year turns 12,000 into 13,200: $1 + \frac{R}{100} = \frac{13200}{12000} = 1.1$. 10% a year.

$P \times 1.1^2 = 12000$, so $P = \frac{12000}{1.21} =$ Rs 9,917.36.

The rate of growth: the percentage by which the price rises each year.

$8000000 \times 1.2^2 = 8000000 \times 1.44 =$ Rs 1,15,20,000.

$27000000 \times 0.8^2 = 27000000 \times 0.64 =$ Rs 1,72,80,000.

No (Rs 1,15,20,000 and Rs 1,72,80,000). Equal when $8000000 \times 1.2^T = 27000000 \times 0.8^T$:
$\left(\frac{1.2}{0.8}\right)^T = \frac{27}{8}$, so $1.5^T = 3.375 = 1.5^3$. After 3 years (both Rs 1,38,24,000).

The price of one unit (or of 10 or 100 units) of a foreign currency in our own currency, decided in Nepal by Nepal Rastra Bank.

110 × 1.1 = Rs 121.

Each dollar gained Rs 11, so he had $\frac{33000}{11} =$ $3,000, bought for 3000 × 110 = Rs 3,30,000.

New rate 110 × 0.9 = 99; 3000 × 99 = 297000. A loss of Rs 33,000.

7.5%: 2 years is in “1 year to 6 years”, and Rs 2,00,000 is more than the least deposit of Rs 75,000.

Half-yearly: 3.75% for 4 periods. $200000 \times 1.0375^4 = 231730.08$: Rs 2,31,730.08.

$200000 + 200000 \times \frac{2 \times 5}{100} =$ Rs 2,20,000.

231730.08 − 220000 = Rs 11,730.08.

Nepal Rastra Bank, the central bank of Nepal.

60000 × 34.83 = Rs 20,89,800.

10%: his deposit is for 1 year, which is in “6 months to 1 year”, and his Rs 20,89,800 is more than the least deposit.

Half-yearly: 5% for 2 periods. $2089800 \times 1.05^2 = 2089800 \times 1.1025 =$ Rs 23,04,004.50.

The increase (in a population or price, or the compound interest) in T years at R% a year.

6000000 × 1.1 × 0.96 = Rs 63,36,000.

With 5%: 6600000 × 0.95 = 6270000. 6336000 − 6270000 = Rs 66,000 more.

$\text{CA} = P\left(1 + \frac{R}{100}\right)^T$

250000 × 1.15 = Rs 2,87,500.

7000 × 28.58 = Rs 2,00,060.

Left after the payment: 287500 − 200060 = 87440. A year later: 87440 × 1.15 = Rs 1,00,556.

After 1 year: 150000 × 1.1 = 165000; left: 165000 − 85000 = 80000.
After the second year: 80000 × 1.1 = Rs 88,000.

Paid in all: 85000 + 88000 = 173000. Interest: 173000 − 150000 = Rs 23,000.

$150000 \times 1.1^2 = 181500$: interest Rs 31,500. 31500 − 23000 = Rs 8,500 more.