myhelper: RS Aggarwal solution class 8 chapter 11 Compound Interest Exercise 11A

Exercise 11A

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Question 1:

Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.

Answer 1:

$Principal for the first year = Rs . 2500 Interest for the first year = Rs . (\frac{2500 \times 10 \times 1}{100}) = Rs . 250 Amount at the end of the first year = Rs . (2500 + 250) = Rs . 2750 Principal for the second year = Rs . 2750 Interest for the second year = Rs . (\frac{2750 \times 10 \times 1}{100}) = Rs . 275 Amount at the end of the second year = Rs . (2750 + 275) = Rs . 3025 ∴ Compound interest = Rs . (3025 - 2500) = Rs . 525$

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Question 2:

Find the amount and the compound interest on Rs 15625 for 3 years at 12% per annum, compounded annually.

Answer 2:

$Principal for the first year = Rs . 15625 Interest for the first year = Rs . (\frac{15625 \times 12 \times 1}{100}) = Rs . 1875 Amount at the end of the first year = Rs . (15625 + 1875) = Rs . 17500 Principal for the second year = Rs . 17500 Interest for the second year = Rs . (\frac{17500 \times 12 \times 1}{100}) = Rs . 2100 Amount at the end of the second year = Rs . (17500 + 2100) = Rs . 19600 Principal for the third year = Rs . 19600 Interest for the third year = Rs . (\frac{19600 \times 12 \times 1}{100}) = Rs . 2352 Amount at the end of the second year = Rs (19600 + 2352) = Rs . 21952 ∴ Compound interest = Rs . (21952 - 15625) = Rs . 6327$

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Question 3:

Find the difference between the simple interest and the compound interest on Rs 5000 for 2 years at 9% per annum.

Answer 3:

$Principal amount = Rs . 5000 Simple interest = Rs . (\frac{5000 \times 2 \times 9}{100}) = Rs . 900 The compound interest can be calculated as follows : Principal for the first year = Rs . 5000 Interest for the first year = Rs . (\frac{5000 \times 9 \times 1}{100}) = Rs . 450 Amount at the end of the first year = Rs . (5000 + 450) = Rs . 5450 Principal for the second year = Rs . 5450 Interest for the second year = Rs . (\frac{5450 \times 9 \times 1}{100}) = Rs . 490.5 Amount at the end of the second year = Rs . (5450 + 490.5) = Rs . 5940.5 ∴ Compound interest = Rs . (5940.5 - 5000) = Rs . 940.5$

$Now, difference between the simple interest and the compound interest$

$= (CI - SI) = Rs . (940.5 - 900) = Rs . 40.5$

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Question 4:

Ratna obtained a loan of Rs 25000 from the Syndicate Bank to renovate her house. If the rate of interest is 8% per annum, what amount will she have to pay to the bank after 2 years to discharge her debt?

Answer 4:

$Principal for the first year = Rs . 25000 Interest for the first year = Rs . (\frac{25000 \times 8 \times 1}{100}) = Rs . 2000 Amount at the end of the first year = Rs . (25000 + 2000) = Rs . 27000 Principal for the second year = Rs . 27000 Interest for the second year = Rs . (\frac{27000 \times 8 \times 1}{100}) = Rs . 2160 Amount at the end of the second year = Rs . (27000 + 2160) = Rs . 29160 Therefore, Ratna has to pay Rs . 29160 after 2 years to discharge her debt .$

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Question 5:

Harpreet borrowed Rs 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.

Answer 5:

$Principal amount = Rs . 20000 Simple interest = Rs . (\frac{20000 \times 2 \times 12}{100}) = Rs . 4800 The compound interest can be calculated as follows : Principal for the first year = Rs . 20000 Interest for the first year = Rs . (\frac{20000 \times 12 \times 1}{100}) = Rs . 2400 Now, amount at the end of the first year = Rs . (20000 + 2400) = Rs . 22400 Principal for the second year = Rs . 22400 Interest for the second year = Rs . (\frac{22400 \times 12 \times 1}{100}) = Rs . 2688 Now, amount at the end of the second year = Rs . (22400 + 2688) = Rs . 25088 Hence, compound interest = Rs . (25088 - 20000) = Rs . 5088 Now, CI - SI = Rs . (5088 - 4800) = Rs . 288 ∴ The amount of money Harpreet will gain after two years is Rs 288 .$

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Question 6:

Manoj deposited a sum of Rs 64000 in a post office for 3 years, compounded annually at $7 \frac{1}{2} %$ per annum. What amount will he get on maturity?

Answer 6:

$Principal for the first year = Rs . 64000 Interest for the first year = Rs . (\frac{64000 \times 15 \times 1}{100 \times 2}) = Rs . 4800 Now, amount at the end of the first year = Rs . (64000 + 4800) = Rs . 68800 Principal for the second year = Rs . 68800 Interest for the second year = Rs . (\frac{68800 \times 15 \times 1}{100 \times 2}) = Rs . 5160 Now, amount at the end of the second year = Rs . (68800 + 5160) = Rs . 73960 Principal for the third year = Rs . 73960 Interest for the third year = Rs . (\frac{73960 \times 15 \times 1}{100 \times 2}) = Rs . 5547 Now, amount at the end of the third year = Rs . (73960 + 5547) = Rs . 79507 ∴ Manoj will get an amount of Rs . 79507 after 3 years .$

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Question 7:

Divakaran deposited a sum of Rs 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.

Answer 7:

$Principal amount = Rs . 6250 Rate of interest = 8 % per annum = 4 % for half year Time = 1 year = 2 half years Principal for the first half year = Rs . 6250 Interest for the first half year = Rs . (\frac{6250 \times 4 \times 1}{100}) = Rs . 250 Now, amount at the end of the first half year = Rs . (6250 + 250) = Rs . 6500 Principal for the second half year = Rs . 6500 Interest for the second half year = Rs . (\frac{6500 \times 4 \times 1}{100}) = Rs . 260 Now, amount at the end of the second half year = Rs (6500 + 260) = Rs . 6760 ∴ Compound interest = Rs (6760 - 6250) = Rs 510 Hence, Divakaran gets a compound interest of Rs 510 .$

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Question 8:

Michael borrowed Rs 16000 from a finance company at 10% per annum, compounded half-yearly. What amount of money will discharge his debt after $1 \frac{1}{2}$ years?

Answer 8:

$Principal amount = Rs . 16000 Rate of interest = 10 % per annum = 5 % for half year Time = 1 \frac{1}{2} years = 3 half y ears$

$Principal for the first half year = Rs . 16000 Interest for the first half year = Rs . (\frac{16000 \times 5 \times 1}{100}) = Rs . 800 Now, amount at the end of the first half year = Rs . (16000 + 800) = Rs . 16800 Principal for the second half year = Rs . 16800 Interest for the second half year = Rs . (\frac{16800 \times 5 \times 1}{100}) = Rs . 840 Now, amount at the end of the second half year = Rs . (16800 + 840) = Rs . 17640 Principal for the third half year = Rs . 17640 Interest for the third half year = Rs . (\frac{17640 \times 5 \times 1}{100}) = Rs . 882 Now, amount at the end of the third half year = Rs . (17640 + 882) = Rs . 18522 ∴ The amount of money Michael has to pay the finance company after 1 \frac{1}{2} years is Rs 18522 .$

RS Aggarwal solution class 8 chapter 11 Compound Interest Exercise 11A

Exercise 11A

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Question 1:

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Question 2:

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Question 7:

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