Mathematics · Chapter 04

66 solved questions

Chapter 4: Currency and Exchange Rate

Every question in this chapter, answered and explained — step-by-step solutions drawn live from the chapter library across 2 question sections.

Exercise 4.135 Mixed Exercises31

Exercise 4.1

1Textbookex4-q1-a

Question 1 What is meant by money exchange?

Money exchange means converting the currency of one country into the currency of another country at an agreed exchange rate, typically through a bank or financial institution.

2Textbookex4-q1-b

Which of the buying rate or selling rate does a Nepali student use to exchange Nepali Rupees into American Dollars while s/he is going for abroad study in America? Write.

Since the student is buying American Dollars from the bank using Nepali Rupees, the bank sells the dollars to the student, so the selling rate is used.

3Textbookex4-q2-a

By using the buying rate of money exchange given above, change the following currency of different countries into Nepali currency: Indian Rupees 1425

India's buying rate is Rs. $160.00$ per $100$ Indian Rupees. $1425 \times \frac{160.00}{100} = Rs. 2, 280$ .

4Textbookex4-q2-b

American Dollar 2000

$2000 \times 127.35 = Rs. 2, 54, 700$ .

5Textbookex4-q2-c

Pound Sterling 4672

$4672 \times 150.94 = Rs. 7, 05, 191.68$ . (Flag: the textbook's own answer key shows Rs. $7, 04, 724.48$ for this part; multiplying the given figures, $4672 \times 150.94$ , correctly gives Rs. $7, 05, 191.68$ , so the printed answer appears to contain a rounding or transcription error — the figure above is the direct calculation from the stated rate.)

6Textbookex4-q2-d

Australian Dollar 672

$672 \times 87.82 = Rs. 59, 015.04$ .

7Textbookex4-q2-e

Saudi Arabian Riyal 1851

$1851 \times 33.91 = Rs. 62, 767.41$ .

8Textbookex4-q2-f

Qatari Riyal 2225

$2225 \times 34.82 = Rs. 77, 474.50$ .

9Textbookex4-q2-g

South Korean Wan 58,230

South Korea's buying rate is Rs. $9.58$ per $100$ Won. $58, 230 \times \frac{9.58}{100} = Rs. 5, 578.43$ .

10Textbookex4-q2-h

Hongkong Dollar 4512

$4512 \times 16.23 = Rs. 73, 229.76$ .

11Textbookex4-q2-i

Malaysian Ringgit 6725

$6725 \times 28.45 = Rs. 1, 91, 326.25$ .

12Textbookex4-q2-j

Chinese Yuan 3450

$3450 \times 18.70 = Rs. 64, 515$ .

13Textbookex4-q3-a

By using the selling rate of money exchange, change Rs. 2,00,000 into the following currencies: Australian Dollar

$\frac{2 , 00 , 000}{88.23} = $2, 266.80$ (Australian).

14Textbookex4-q3-b

American Dollar

$\frac{2 , 00 , 000}{127.95} = $1, 563.11$ (American).

15Textbookex4-q3-c

Euro

$\frac{2 , 00 , 000}{128.73} = €1, 553.64$ .

16Textbookex4-q3-d

United Arab Emirates Dirham

$\frac{2 , 00 , 000}{34.83} = 5, 742.18$ Dirham.

17Textbookex4-q4-a

According to the exchange rate declared by Nepal Rastra Bank on a specific day, the buying and selling rate for 1 American Dollar are Rs. 127.50 and Rs. 128 respectively, How many American Dollars can be exchanged for Rs. 81,280?

Buying dollars with rupees uses the selling rate: $\frac{81 , 280}{128} = $635$ .

18Textbookex4-q4-b

Find how many Nepali Rupees can you exchange with American Dollar 600?

Selling dollars for rupees uses the buying rate: $600 \times 127.50 = Rs. 76, 500$ .

19Textbookex4-q5-a

According to the exchange rate declared by Nepal Rastra bank on 23 August 2022, the buying and selling rate for Chinese Yuan 1 are Rs. 18.64 and Rs. 18.73 respectively, How many Chinese Yuan can be exchanged for Rs. 37,460?

Buying Yuan with rupees uses the selling rate: $\frac{37 , 460}{18.73} = 2, 000$ Yuan.

20Textbookex4-q5-b

How many Nepalese rupees can you exchange with Chinese Yuan 5000?

Selling Yuan for rupees uses the buying rate: $5000 \times 18.64 = Rs. 93, 200$ .

21Textbookex4-q6-a

Using the above-mentioned exchange rate table, answer the following questions: How many United Emirates Dirhams are equal to 1 Euro?

Sell 1 Euro for rupees (buying rate): $1 \times 128.13 = Rs. 128.13$ . Buy Dirham with this (selling rate): $\frac{128.13}{34.83} = 3.68$ Dirham.

22Textbookex4-q6-b

How many Malaysian Ringgits are equal to 1 Qatari Riyal?

Sell 1 Qatari Riyal for rupees (buying rate): $1 \times 34.82 = Rs. 34.82$ . Buy Ringgit with this (selling rate): $\frac{34.82}{28.58} = 1.22$ Ringgit.

23Textbookex4-q6-c

How many Canadian Dollars are equal to 200 American Dollar?

Sell 200 American Dollars for rupees (buying rate): $200 \times 127.35 = Rs. 25, 470$ . Buy Canadian Dollars with this (selling rate): $\frac{25 , 470}{98.54} = 258.47$ Canadian Dollars.

24Textbookex4-q6-d

How many Thai Bhatts are equal to 200 Pound Sterling?

Sell 200 Pound Sterling for rupees (buying rate): $200 \times 150.94 = Rs. 30, 188$ . Buy Thai Bhat with this (selling rate): $\frac{30 , 188}{3.59} = 8, 408.91$ Bhat.

25Textbookex4-q7-a

Sobita went to Australia from Nepal for her higher studies. After completing her studies, she has been working as a secondary level teacher. She earns 37 Australian Dollar per hour. She teaches 5 hours a day except Sunday. If exchange rate of the Australian Dollar 1 = Rs. 90, How much salary does she have in Nepali Rupees for a week?

She teaches 6 days a week (every day except Sunday), 5 hours a day, at $37/hour: weekly earning $= 37 \times 5 \times 6 = $1, 110$ . In rupees (at Rs. 90/dollar): $1, 110 \times 90 = Rs. 99, 900$ .

26Textbookex4-q7-b

Find how much monthly salary does she have in Nepali Rupees?

Taking a month as (approximately) 5 such weeks: monthly salary $= 99, 900 \times 5 = Rs. 4, 99, 500$ .

27Textbookex4-q8-a

Question 8 An American businessman exchanged American Dollar for NRs. 12,40,000 at the exchange rate of American Dollar 1 = NRs. 124. After a week, Nepali currency is inflated by 10%. At that time, he exchanged the dollar into Nepali currency, then how much loss or profit have? Find it.

$ amount $= \frac{12 , 40 , 000}{124} = $10, 000$ . Nepali currency inflated by $10%$ means the new rate is $124 \times 1.10 = Rs. 136.4$ per dollar. Converting back: $10, 000 \times 136.4 = Rs. 13, 64, 000$ . Profit $= 13, 64, 000 - 12, 40, 000 = Rs. 1, 24, 000$ .

28Textbookex4-q8-b

A businessman buys goods from Thailand. For this, he exchanged Nepali currency Rs. 7,20,000 at the exchange rate 1 Thai Bhatt = NRs. 3.60. After a day, Nepali currency is deflated by 5%. Due to the inadequate circumstances of the country, he wishes not to buy the goods from Thailand. So that at that time of deflation, if he again exchanged the Thai Bhatt into Nepali currency, how much loss or profit will he have? Find it.

Bhat amount $= \frac{7 , 20 , 000}{3.60} = 2, 00, 000$ Bhat. Nepali currency deflated by $5%$ means the new rate is $3.60 \times (1 - 0.05) = Rs. 3.42$ per Bhat. Converting back: $2, 00, 000 \times 3.42 = Rs. 6, 84, 000$ . Loss $= 7, 20, 000 - 6, 84, 000 = Rs. 36, 000$ .

29Textbookex4-q9-a

Question 9 A Nepali went to visit the UAE. In that time, he purchased a branded television of 75 inch for 10,000 Dirham. The exchange rate of that day was UAE Dirham 1 = NRs. 34.50. He paid 20% custom tax and 13% VAT. His relative wishes to buy it. At what price should he sell at break-even? Find it.

Cost in NRs $= 10, 000 \times 34.50 = Rs. 3, 45, 000$ . Adding $20%$ custom tax: $3, 45, 000 \times 1.20 = Rs. 4, 14, 000$ . Adding $13%$ VAT on this: $4, 14, 000 \times 1.13 = Rs. 4, 67, 820$ . To break even, he should sell it for Rs. $4, 67, 820$ .

30Textbookex4-q9-b

20% profit can be gained at a good sold for Indian rupees 21,600. At what Nepalese rupees can it be sold to gain 25% profit?

Cost price in Indian Rupees $= \frac{21 , 600}{1.20} = 18, 000$ IC. Selling price for $25%$ profit $= 18, 000 \times 1.25 = 22, 500$ IC. Converting to Nepali Rupees using the exchange table (India: Rs. $160.00$ per $100$ IC): $22, 500 \times \frac{160.00}{100} = Rs. 36, 000$ .

31Textbookex4-q10-a

Question 10 A Nepali does business in Australia. He came to Nepal for his household work. He wished to take 500 Pasmina shawls while returning back. He purchased the shawls at the rate of Rs. 3,500 each. He took it in Australia by paying 5% export tax. He paid Australian Dollar 30 for transportation from the airport to his residence. He sold the shawls at the rate of Australian Dollar 80 for each, find the loss or profit percent he got. (Australian dollar 1 = NRs. 88.50)

Cost of 500 shawls $= 500 \times 3, 500 = Rs. 17, 50, 000$ . Adding $5%$ export tax: $17, 50, 000 \times 1.05 = Rs. 18, 37, 500$ . Converting to Australian Dollars: $\frac{18 , 37 , 500}{88.50} = 20, 762.71$ AUD. Adding transport cost: $20, 762.71 + 30 = 20, 792.71$ AUD total cost. Revenue from selling: $500 \times 80 = 40, 000$ AUD. Profit $= 40, 000 - 20, 792.71 = 19, 207.29$ AUD. Profit percent $= \frac{19 , 207.29}{20 , 792.71} \times 100% \approx 92.37%$ .

32Textbookex4-q10-b

The fare of air ticket from Kathmandu to Bangkok of Nepal Airlines is Rs. 28,000. Again, if the same ticket can be bought for 8000 Thai Bhat for Thailand, what percentage is it cheaper to buy the ticket from which place? (Thai Bhatt 1 = NRs. 3.50)

Flag: the numbers as given reproduce the exact same price both ways — $8000 \times 3.50 = Rs. 28, 000$ , identical to the Nepal Airlines fare of Rs. $28, 000$ — so there is no percentage difference between the two, which does not match the textbook's own printed answer of " $6.97%$ cheaper in Kathmandu"; that figure cannot be reproduced from the stated Rs. $28, 000$ , $8000$ Bhat, and rate of Rs. $3.50$ per Bhat. Direct calculation: Thailand price in NRs $= 8000 \times 3.50 = Rs. 28, 000$ , exactly equal to the Kathmandu price, so the two are the same price.

33Textbookex4-q11-a

Question 11 If the American Dollar 176 = 100 Pound Sterling and Pound Sterling 1 = Nepali Rupees 151, how many Nepali Rupees can be exchanged for 132 American Dollars?

$$176 = 100£$ , so $$1 = \frac{100}{176} £$ . Also $£1 = Rs. 151$ . So $$1 = \frac{100}{176} \times 151 = Rs. 85.80$ (approx). For $$132$ : $132 \times \frac{100}{176} \times 151 = Rs. 11, 325$ .

34Textbookex4-q11-b

If I.C. 100 = NRs. 160 and 1 American Dollar = NRs. 120, how many American Dollars are equal to I.C. 7500?

I.C. $7500 \to$ NRs $= 7500 \times \frac{160}{100} = Rs. 12, 000$ . Converting to Dollars: $\frac{12 , 000}{120} = $100$ .

35Textbookex4-q11-c

If Chinese Yuan 1 = NRs. 18.70 and UAE Riyal 1 = NRs. 33.91, then change the Chinese Yuan 5612 into the United Arab Emirates Riyal.

Yuan $5612 \to$ NRs $= 5612 \times 18.70 = Rs. 1, 04, 944.40$ . Converting to UAE Riyal: $\frac{1 , 04 , 944.40}{33.91} = 3, 094.79$ Riyal.

Mixed Exercises

1Textbookmixed-cur-q1-a

A family wants to deposit Rs. 4,00,000 in the account of a child aged who has just started grade 11. The money is intended for his/her study. If the money is deposited with the agreement that the amount with principal and interest would be drawn after he/she passed grade 12 at the age of 19. Then, a Development Bank offers three alternatives: First offer — rate of compound interest is 19% per annum. Second offer — rate of compound interest is 18% per annum compounded semi-annually. Third offer — rate of simple interest is 20% per annum. How many times will the interest be calculated in 2 years according to the half yearly compound interest? Write.

For half yearly compounding, interest is calculated twice a year, so over 2 years it is calculated $2 \times 2 = 4$ times.

2Textbookmixed-cur-q1-b

Which of the following alternatives would you suggest to your parents to deposit the money and why? Justify with calculation.

The deposit period is $T = 2$ years (grade 11 to after passing grade 12). $P = Rs. 4, 00, 000$ . First offer ( $19%$ p.a. CI): $C I = 4, 00, 000 [(1.19)^{2} - 1] = Rs. 1, 66, 440$ . Second offer ( $18%$ p.a. compounded semi-annually, so $9%$ per half-year over 4 periods): $C I = 4, 00, 000 [(1.09)^{4} - 1] \approx Rs. 1, 64, 632.64$ . Third offer ( $20%$ p.a. simple interest): $S I = \frac{4 , 00 , 000 \times 2 \times 20}{100} = Rs. 1, 60, 000$ . Comparing all three, the first offer gives the highest interest (Rs. $1, 66, 440$ ), so I would suggest depositing according to the first offer.

3Textbookmixed-cur-q2-a

A sum of money amounts to Rs. 12,000 and Rs. 13,200 in 2 years and 3 years respectively at a certain rate of interest compounded annually. Write the formula to find the compound interest.

$C I = P [(1 + \frac{R}{100})^{T} - 1]$ .

4Textbookmixed-cur-q2-b

What should be the rate of the compound interest?

Let $P (1 + \frac{R}{100})^{2} = 12, 000$ and $P (1 + \frac{R}{100})^{3} = 13, 200$ . Dividing: $1 + \frac{R}{100} = \frac{13 , 200}{12 , 000} = 1.10$ , so $R = 10%$ .

5Textbookmixed-cur-q2-c

What should be the principal?

$P = \frac{12 , 000}{( 1.10 ) ^{2}} = \frac{12 , 000}{1.21} \approx Rs. 9, 917.35$ .

6Textbookmixed-cur-q3-a

A man bought a land at Rs. 80,00,000 on 25th Baisakh of 2075 BS and started construction of a house on the same day. The construction of the house completed at the cost of Rs. 2,70,00,000. The price of land increased at the rate of 20% per year and the price of house decreased at the rate of 20% per year. What does R indicate in the price after T years $(P_{T}) = P (1 + \frac{R}{100})^{T}$ ?

$R$ indicates the yearly growth (or depreciation) rate of the price.

7Textbookmixed-cur-q3-b

What will be the price of the land after 2 years?

Land: $P = Rs. 80, 00, 000$ , $R = 20%$ (growth), $T = 2$ years. $P_{2} = 80, 00, 000 (1.20)^{2} = Rs. 1, 15, 20, 000$ .

8Textbookmixed-cur-q3-c

What will be the price of the house after 2 years?

House: $V_{0} = Rs. 2, 70, 00, 000$ , $R = 20%$ (depreciation), $T = 2$ years. $V_{2} = 2, 70, 00, 000 (0.80)^{2} = Rs. 1, 72, 80, 000$ .

9Textbookmixed-cur-q3-d

Will the prices of the land and house be the same after 2 years? If not, in how many years will the prices of the land and house be equal?

No, the prices are not equal after 2 years (Rs. $1, 15, 20, 000$ for land vs Rs. $1, 72, 80, 000$ for the house). Setting them equal: $80, 00, 000 (1.20)^{T} = 2, 70, 00, 000 (0.80)^{T}$ , so $(\frac{1.20}{0.80})^{T} = \frac{2 , 70 , 00 , 000}{80 , 00 , 000} = 3.375$ , i.e. $(1.5)^{T} = 3.375$ . Since $(1.5)^{3} = 3.375$ , $T = 3$ years. So the prices of the land and house will be equal after 3 years.

10Textbookmixed-cur-q4-a

Ram exchanged some Nepali rupees with American dollars at the exchange rate of $1 = Rs. 110. After 5 days, Nepali currency devalued against American dollars by 10% and he made a profit of Rs. 33,000 by exchanging the same dollars into Nepali currency again. What is meant by exchange rate of currency?

The exchange rate of currency is the rate (price) at which the currency of one country can be exchanged for the currency of another country.

11Textbookmixed-cur-q4-b

How much Nepalese rupees are equal to one American dollar ($1) after devaluation of the Nepali currency?

Devaluation of Nepali currency by $10%$ against the dollar means more rupees are needed per dollar: new rate $= 110 \times 1.10 = Rs. 121$ per dollar.

12Textbookmixed-cur-q4-c

Find how much Nepali rupees did Ram exchange with American dollars at first?

Let the initial amount exchanged $= x$ . Dollars received $= \frac{x}{110}$ . Converting these dollars back at the new rate of Rs. $121$ : value $= \frac{x}{110} \times 121 = 1.1 x$ . Profit $= 1.1 x - x = 0.1 x$ . Setting $0.1 x = 33, 000$ : $x = Rs. 3, 30, 000$ .

13Textbookmixed-cur-q4-d

How much profit or loss would be there for him, if the Nepali rupees had revalued by 10% instead of devaluation of 10%?

If instead the Nepali rupees revalued by $10%$ , the new rate would be $110 \times (1 - 0.10) = Rs. 99$ per dollar. Converting back: value $= \frac{x}{110} \times 99 = 0.9 x$ . Loss $= x - 0.9 x = 0.1 x = 0.1 \times 3, 30, 000 = Rs. 33, 000$ loss.

14Textbookmixed-cur-q5-a

The management committee of Nepal Bank Limited in its regular meeting has decided to change its annual policy slightly. According to the decision, the rate of interest for fixed deposit compounded semi annually is given below: Up to 6 months: 6.75%, minimum deposit Rs. 50,000. From 6 months to 1 year: 7.25%, minimum deposit Rs. 50,000. From 1 year to 6 years: 7.5%, minimum deposit Rs. 75,000. Sujit Thakur borrowed Rs. 2,00,000 from a cooperative on condition of paying it back in 2 years at the rate of simple interest of 5%. Immediately after borrowing, he deposited the same sum in a fixed deposit account of Nepal Bank Limited for the same duration. Which rate of interest should Sujit Thakur deposit the money in the fixed deposit?

Since the deposit period is 2 years (falling in the "1 year to 6 years" bracket), the applicable rate is $7.5%$ . Flag: the deposit table is described as compounded semi-annually, so the mathematically consistent computation for a 2-year term at 7.5% p.a. would use 4 half-year periods at 3.75% each, giving $C A = 2, 00, 000 (1.0375)^{4} \approx Rs. 2, 31, 730.08$ . However, the textbook's own printed answer (Rs. $2, 31, 125$ ) is instead reproduced exactly by simple annual compounding, $C A = 2, 00, 000 (1.075)^{2} = Rs. 2, 31, 125$ — the figures below follow the book's own answer (annual compounding) so that parts (c) and (d) stay consistent with it, but this is an inconsistency in the source between the stated semi-annual compounding and the number actually used.

15Textbookmixed-cur-q5-b

Find the compound amount that Sujit Thakur could receive in 2 years.

$C A = 2, 00, 000 (1.075)^{2} = Rs. 2, 31, 125$ (see flag above).

16Textbookmixed-cur-q5-c

Find the total amount to be paid to cooperative in 2 years.

Simple interest on the loan: $S I = \frac{2 , 00 , 000 \times 2 \times 5}{100} = Rs. 20, 000$ . Total to be paid $= 2, 00, 000 + 20, 000 = Rs. 2, 20, 000$ .

17Textbookmixed-cur-q5-d

How much profit did Sujit Thakur earn in 2 years?

Profit (interest earned on the deposit) $= C A - P = 2, 31, 125 - 2, 00, 000 = Rs. 31, 125$ .

18Textbookmixed-cur-q6-a

Anish has returned back to Nepal from United Arab Emirate after 5 years. He earned 60,000 United Arab Emirate Dirhams and exchanged it with the Nepali rupees at the exchange rate of 1 Dirham = Rs. 34.83. He deposited the sum in the fixed deposit account of Nepal Bank for 1 year as per the following rate of interest compounded semi-annually: Up to 6 months: 9%, minimum deposit Rs. 50,000. From 6 months to 1 year: 10%, minimum deposit Rs. 50,000. From 1 year to 5 years: 12%, minimum deposit Rs. 75,000. Which body of government decides the exchange rate of currency in our country?

The exchange rate of currency in Nepal is decided by Nepal Rastra Bank, the central bank of Nepal.

19Textbookmixed-cur-q6-b

How much Nepali rupees did Anish receive by exchanging 60,000 United Arab Emirate Dirhams?

$60, 000 \times 34.83 = Rs. 20, 89, 800$ .

20Textbookmixed-cur-q6-c

Which deposit offer of the bank is applicable for Anish? Give reason.

A deposit for exactly 1 year falls at the boundary of the "6 months to 1 year" bracket, so the applicable rate is $10%$ .

21Textbookmixed-cur-q6-d

How much amount will Anish receive from the bank after 1 year?

Since the rate is $10%$ p.a. compounded semi-annually over 1 year (2 periods at $5%$ ): $C A = 20, 89, 800 (1.05)^{2} = Rs. 23, 04, 004.50$ .

22Textbookmixed-cur-q7-a

The price of a piece of land in Kathmandu was fixed at Rs. 60,00,000 at the end of 2020 AD. The price increased by 10% as the consequence of increasing buying pressure at beginning of 2021. But the price of land decreased by 4% due to the economic crisis at the end of 2022 AD. What does $P (1 + \frac{R}{100})^{T} - P$ as per usual notation indicate?

$P (1 + \frac{R}{100})^{T} - P$ indicates the increase in price (the growth amount) after $T$ years — it is the compound interest / growth formula applied to price, i.e. $C A - P$ .

23Textbookmixed-cur-q7-b

What will be the price of the land at the end of 2022?

First, the price rises $10%$ at the beginning of 2021: $60, 00, 000 \times 1.10 = Rs. 66, 00, 000$ . Then it falls $4%$ by the end of 2022: $66, 00, 000 \times (1 - 0.04) = 66, 00, 000 \times 0.96 = Rs. 63, 36, 000$ .

24Textbookmixed-cur-q7-c

How much loss will be there to the person if the price decreased by 5% instead of decreasing by 4% in 2022 AD?

With a $5%$ decrease instead: $66, 00, 000 \times (1 - 0.05) = 66, 00, 000 \times 0.95 = Rs. 62, 70, 000$ . Extra loss compared to the $4%$ case $= 63, 36, 000 - 62, 70, 000 = Rs. 66, 000$ .

25Textbookmixed-cur-q8-a

Kul Bahadur decided to go for foreign employment and lent (borrowed) a sum of Rs. 2,50,000 for 2 years at the interest rate of 15% compounded annually from a cooperative bank. After 1 year, he remitted 7,000 Ringgits to his home from the saving. Write the formula to find the compound amount.

$C A = P (1 + \frac{R}{100})^{T}$ . Note: part (c) uses the exchange table's selling rate for Malaysian Ringgit (Rs. 28.58), and the answer to part (d) assumes the remitted amount (converted to rupees) is applied against the loan balance after 1 year, with the remainder then compounding for the second year.

26Textbookmixed-cur-q8-b

What is the total amount to be paid after 1 year?

$C A_{1} = 2, 50, 000 (1.15)^{1} = Rs. 2, 87, 500$ .

27Textbookmixed-cur-q8-c

How much Nepali rupees are equal to Malaysian Ringgits 7,000?

$7, 000 \times 28.58 = Rs. 2, 00, 060$ (using the selling rate for Ringgit, see note above).

28Textbookmixed-cur-q8-d

How much total amount should he pay to clear all the debts finally?

Balance after 1 year: $2, 87, 500 - 2, 00, 060 = Rs. 87, 440$ . Compounding this for the second year at $15%$ : $87, 440 \times 1.15 = Rs. 1, 00, 556$ . So he should pay Rs. $1, 00, 556$ to clear all debts finally.

29Textbookmixed-cur-q9-a

A person lent a sum of Rs. 1,50,000 for 2 years at the interest rate of 10% per annum compounded annually. He paid Rs. 85,000 at the end of the first year. How much total amount should he pay to clear all the debts at the end of second year?

Amount at end of year 1: $1, 50, 000 \times 1.10 = Rs. 1, 65, 000$ . Subtracting the Rs. $85, 000$ paid: balance $= 1, 65, 000 - 85, 000 = Rs. 80, 000$ . Compounding for year 2: $80, 000 \times 1.10 = Rs. 88, 000$ .

30Textbookmixed-cur-q9-b

Find the total interest that he paid in two years.

Total paid $= 85, 000 + 88, 000 = Rs. 1, 73, 000$ . Total interest $= 1, 73, 000 - 1, 50, 000 = Rs. 23, 000$ .

31Textbookmixed-cur-q9-c

If he cleared all the debts only after two years, how much more or less interest should have been paid?

If cleared only after 2 years with no interim payment, interest would be $C I = 1, 50, 000 [(1.10)^{2} - 1] = 1, 50, 000 \times 0.21 = Rs. 31, 500$ . Compared to the actual interest paid (Rs. $23, 000$ ), this is Rs. $31, 500 - 23, 000 = Rs. 8, 500$ more.

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