Class 8 RD Sharma Solutions - Chapter 14 Compound Interest - Exercise 14.1

Exercise 14.1 of Chapter 14 in RD Sharma Solutions for Class 8 focuses on compound interest calculations. This exercise introduces students to the concept of compound interest and its applications in various financial scenarios.

What is Compound Interest?

Compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods. It's essentially "interest on interest." This concept is widely used in banking, investments, and loans.

Question 1. Find the compound interest when principal = Rs 3000, rate = 5% per annum and time = 2 years.

Solution:

Given that,

Principal (p) = Rs 3000

Rate (r) = 5%

Time = 2years

Interest for first year = (3000×5×1)/100 = 150

Amount at the end of first year = 3000 + 300 = Rs 3150

Principal Interest for Second year = (3150×5×1)/100 = 157.5

Amount at the end of Second year = 3150 + 157.5 = Rs 3307.5

Compound Interest(CI) = 3307.5 – 3000 = Rs 307.5

Question 2. What will be the compound interest on Rs. 4000 in two years when rate of interest is 5% per annum?

Solution: 

Given that,

Principal (p) = Rs 4000

Rate (r) = 5%

Time = 2 years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 4000 (1 + 5/100)^2

= 4000 (105/100)^2

= Rs 4410

Compound Interest(CI) = A – P = 4410 – 4000 = Rs 410

Question 3. Rohit deposited Rs. 8000 with a finance company for 3 years at an interest of 15% per annum. What is the compound interest that Rohit gets after 3 years?

Solution: 

Given that,

Principal (p) = Rs 8000

Rate (r) = 15%

Time = 3years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 8000 (1 + 15/100)^3

= 8000 (115/100)^3

= Rs 12167

Compound Interest(CI) = A – P = 12167 – 8000 = Rs 4167

Question 4. Find the compound interest on Rs. 1000 at the rate of 8% per annum for 1 ½ years when interest is compounded half-yearly.

Solution: 

Given that,

Principal (p) = Rs 1000

Rate (r) = 8%

Time = 1 ½ years = 3/2 × 2 = 3 half year

Using formula A = P (1 + R/100)²ⁿ, put all values in these formula

= 1000 (1 + 8/200)³

= 1000 (208/200)³

= Rs 1124.86

Compound Interest(CI) = A – P = 1124.86 – 1000 = Rs 124.86

Question 5. Find the compound interest on Rs. 160000 for one year at the rate of 20% per annum, if the interest is compounded quarterly.

Solution: 

Given that,

Principal (p) = Rs 160000

Rate (r) = 20% = 20/4 = 5% (for quarter year)

Time = 1year = 1 × 4 = 4 quarters

Using formula A = P (1 + R/100)ⁿ , put all values in these formula 

= 160000 (1 + 5/100)⁴

= 160000 (105/100)⁴

= Rs 194481

Compound Interest(CI) = A – P = 194481 – 160000 = Rs 34481

Question 6. Swati took a loan of Rs. 16000 against her insurance policy at the rate of 12 ½ % per annum. Calculate the total compound interest payable by Swati after 3 years.

Solution: 

Given that,

Principal (p) = Rs 16000

Rate (r) = 12 ½ % = 12.5%

Time = 3years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 16000 (1 + 12.5/100)³

= 16000 (112.5/100)³

= Rs 22781.25

Compound Interest(CI) = A – P = 22781.25 – 16000 = Rs 6781.25

Question 7. Roma borrowed Rs. 64000 from a bank for 1 ½ years at the rate of 10% per annum. Compare the total compound interest payable by Roma after 1 ½ years, if the interest is compounded half-yearly

Solution: 

Given that,

Principal (p) = Rs 64000

Rate (r) = 10 % = 10/2 % (for half a year)

Time = 1 ½ years = 3/2 × 2 = 3 (half year)

Using formula A = P (1 + R/100)ⁿ , put all values in these formula

= 64000 (1 + 10/2×100)³

= 64000 (210/200)³

= Rs 74088

Compound Interest = A – P = 74088 – 64000 = Rs 10088

Question 8.  Mewa lal borrowed Rs. 20000 from his friend Rooplal at 18% per annum simple interest. He lent it to Rampal at the same rate but compounded annually. Find his gain after 2 years.

Solution: 

Given that,

Principal (p) = Rs 20000

Rate (r) = 18 %

Time = 2 years

By using the formula,

Interest amount Mewa lal has to pay,

Using formula Simple interest = P×T×R/100

= (20000×18×2)/100 = 7200

The interest amount Rampal has to pay to Mewa lal is Rs. 7200

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 20000 (1 + 18/100)2 = 20000 (118/100)²

= Rs 27848 – 20000 = Rs 7848

= 7848 – 7200 = Rs 648

Mewa lal earn Rs 648

Question 9. Find the compound interest on Rs. 8000 for 9 months at 20% per annum compounded quarterly.

Solution: 

Given that,

Principal (p) = Rs 8000

Rate (r) = 20 % = 20/4 = 5% 

Time = 9 months = 9/3 = 3 

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 8000 (1 + 5/100)³

= 8000 (105/100)³

= Rs 9261

Compound Interest(CI) = A – P =  9261 – 8000 = Rs 1261

Question 10. Find the compound interest at the rate of 10% per annum for two years on that principal which in two years at the rate of 10% per annum given Rs. 200 as simple interest

Solution: 

Given that,

Simple interest (SI) = Rs 200

Rate (r) = 10 %

Time = 2 years

Here we will use Simple interest = P×T×R/100 formula

P = (SI × 100)/ T×R

= (200 × 100) / 2 × 10 = Rs 1000

As given that Rate of compound interest = 10%

Time = 2years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula 

= 1000 (1 + 10/100)²

= 1000 (110/100)² = Rs 1210

Compound Interest(CI) = A – P = 1210 – 1000 = Rs 210

Question 11. Find the compound interest on Rs. 64000 for 1 year at the rate of 10% per annum compounded quarterly.

Solution: 

Given that,

Principal (p) = Rs 64000

Rate (r) = 10 % = 10/4 % (for quarterly)

Time = 1year = 1× 4 = 4 (for quarter in a year)

Using formula A = P (1 + R/100)ⁿ , put all values in these formula

= 64000 (1 + 10/4×100)⁴

= 64000 (410/400)⁴

= Rs 70644.03

Compound Interest(CI) = A – P = 70644.03 – 64000 = Rs 6644.03

Question 12. Ramesh deposited Rs. 7500 in a bank which pays him 12% interest per annum compounded quarterly. What is the amount which he receives after 9 months.

Solution: 

Given that,

Principal (p) = Rs 7500

Rate (r) = 12 % = 12/4 = 3 % (for quarterly)

Time = 9 months = 9/12years = 9/12 × 4 = 3 (for quarter in a year)

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 7500 (1 + 3/100)³

= 7500 (103/100)³ = Rs 8195.45

Hence, the Required amount is Rs 8195.45

Question 13. Anil borrowed a sum of Rs. 9600 to install a hand pump in his dairy. If the rate of interest is 5 ½ % per annum compounded annually, determine the compound interest which Anil will have to pay after 3 years.

Solution: 

Given that,

Principal (p) = Rs 9600

Rate (r) = 5 ½ % = 11/2 %

Time = 3years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 9600 (1 + 11/2×100)³

= 9600 (211/200)³ = Rs 11272.71

Compound Interest (CI)= A – P = 11272.71 – 9600 = Rs 1672.71

Question 14. Surabhi borrowed a sum of Rs. 12000 from a finance company to purchase a refrigerator. If the rate of interest is 5% per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.

Solution:

Given that,

Principal (p) = Rs 12000

Rate (r) = 5 %

Time = 3years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 12000 (1 + 5/100)³

= 12000 (105/100)³ = Rs 13891.5

Compound Interest(CI) = A – P = 13891.5 – 12000 = Rs 1891.5

Question 15. Daljit received a sum of Rs. 40000 as a loan from a finance company. If the rate of interest is 7% per annum compounded annually, calculate the compound interest that Daljit pays after 2 years.

Solution:

Given that,

Principal (p) = Rs 40000

Rate (r) = 7%

Time = 2years

Using formula A = P (1 + R/100)ⁿ, put all values in these formula

= 40000 (1 + 7/100)²

= 40000 (107/100)² = Rs 45796

Compound Interest(CI)= A – P = 45796 – 40000 = Rs 579

Summary

Exercise 14.1 of Chapter 14 in RD Sharma Solutions for Class 8 covers fundamental and moderately complex problems on compound interest. It includes calculations of interest, amount, rate, time, and comparisons with simple interest. The problems also touch upon real-world applications like population growth and loan repayments, helping students understand the practical relevance of compound interest.