Class 8 RD Sharma Solutions - Chapter 14 Compound Interest - Exercise 14.2 | Set 1

Chapter 14 of RD Sharma's Class 8 Mathematics textbook explores the concept of Compound Interest a fundamental topic in financial mathematics. Exercise 14.2 | Set 1 provides practice problems to help students understand how to calculate compound interest which is crucial for managing savings and investments. This exercise builds on the principles of interest calculation and helps students apply these concepts in real-world scenarios.

What is Compound Interest?

The Compound Interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from the previous periods. Unlike simple interest which is calculated only on the principal amount, compound interest grows over time as interest is added to the principal resulting in the interest being calculated on the new total.

Question 1. Compute the amount and the compound interest in each of the following by using the formulae when:
(i) Principal = Rs 3000, Rate = 5%, Time = 2 years
(ii) Principal = Rs 3000, Rate = 18%, Time = 2 years
(iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years
(iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years
(v) Principal = Rs 12800, Rate = 7 ½ %, Time = 3 years
(vi) Principal = Rs 10000, Rate = 20% per annum compounded half-yearly, Time = 2 years
(vii) Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half yearly, Time = 2 years.

Solution:

We have,

A = P (1 + R/100)ⁿ

Let us solve

(i) Given, P = Rs 3000, rate = 5%, time = 2years
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 3000 (1 + 5/100)²
= 3000 (105/100)²
= Rs 3307.5

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 3307.5 – 3000 = Rs 307.5

(ii) Given, P = Rs 3000, rate = 18%, time = 2years
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 3000 (1 + 18/100)²
= 3000 (118/100)²
= Rs 4177.2

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 4177.2 – 3000 = Rs 1177.2

(iii) Given, P = Rs 5000, rate = 10%, time = 2years
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 5000 (1 + 10/100)²
= 5000 (110/100)²
= Rs 6050

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 6050 – 5000 = Rs 1050

(iv) Given, P = Rs 2000, rate = 4%, time = 3years
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 2000 (1 + 4/100)³
= 2000 (104/100)³
= Rs 2249.72

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 2249.72 – 2000 = Rs 249.72

(v) Given, P = Rs 12800, rate = 7 ½ % = 15/2% = 7.5%, time = 3years
A = P (1 + R/100)ⁿ
= 12800 (1 + 7.5/100)³
= 12800 (107.5/100)³
= Rs 15901.4
Compound interest (CI) = A-P = Rs 15901.4 – 12800 = Rs 3101.4

(vi) Given, P = Rs 10000, rate = 20 % = 20/2 = 10% (quarterly), time = 2years = 2 × 2 = 4years
A = P (1 + R/100)ⁿ
= 10000 (1 + 10/100)⁴
= 10000 (110/100)⁴
= Rs 14641

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 14641 – 10000 = Rs 4641

(vii) Given, P = Rs 160000, rate = 10% = 10/2% = 5% (half-yearly), time = 2years = 2×2 = 4 quarters
A = P (1 + R/100)ⁿ
= 160000 (1 + 5/100)⁴
= 160000 (105/100)⁴
= Rs 194481

Solving for Compound Interest, we get 
Compound interest (CI) = A-P = Rs 194481 – 160000 = Rs 34481

Question 2. Find the amount of Rs. 2400 after 3 years, when the interest is compounded annually at the rate of 20% per annum.

Solution:

Given is the following set of values,
Principal (p) = Rs 2400
Rate (r) = 20% per annum
Time (t) = 3 years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 2400 (1 + 20/100)³
= 2400 (120/100)³
= Rs 4147.2
∴ Amount is Rs 4147.2

Question 3. Rahman lent Rs. 16000 to Rasheed at the rate of 12 ½ % per annum compound interest. Find the amount payable by Rasheed to Rahman after 3 years.

Solution:

Given :
Principal (p) = Rs 16000
Rate (r) = 12 ½ % per annum = 12.5%
Time (t) = 3 years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 16000 (1 + 12.5/100)³
= 16000 (112.5/100)³
= Rs 22781.25
∴ Amount is Rs 22781.25

Question 4. Meera borrowed a sum of Rs. 1000 from Sita for two years. If the rate of interest is 10% compounded annually, find the amount that Meera has to pay back.

Solution:

We have,
Principal (p) = Rs 1000
Rate (r) = 10 % per annum
Time (t) = 2 years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 1000 (1 + 10/100)²
= 1000 (110/100)²
= Rs 1210
∴ Amount is Rs 1210

Question 5. Find the difference between the compound interest and simple interest. On a sum of Rs. 50,000 at 10% per annum for 2 years.

Solution:

Given details are,
Principal (p) = Rs 50000
Rate (r) = 10 % per annum
Time (t) = 2 years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 50000 (1 + 10/100)²
= 50000 (110/100)²
= Rs 60500

Calculating for Compound Interest, we have
CI = Rs 60500 – 50000 = Rs 10500
We know that SI = (PTR)/100 = (50000 × 10 × 2)/100 = Rs 10000
∴ Difference amount between CI and SI = 10500 – 10000 = Rs 500

Question 6. Amit borrowed Rs. 16000 at 17 ½ % per annum simple interest. On the same day, he lent it to Ashu at the same rate but compounded annually. What does he gain at the end of 2 years?

Solution:

Given details are,
Principal (p) = Rs 16000
Rate (r) = 17 ½ % per annum = 35/2% or 17.5%
Time (t) = 2 years
Interest paid by Amit = (PTR)/100 = (16000×17.5×2)/100 = Rs 5600
Amount gained by Amit:
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 16000 (1 + 17.5/100)²
= 16000 (117.5/100)²
= Rs 22090

Calculating for Compound Interest, we have
CI = Rs 22090 – 16000 = Rs 6090
∴ Amit's total gain is = Rs 6090 – 5600 = Rs 490

Question 7. Find the amount of Rs. 4096 for 18 months at 12 ½ % per annum, the interest being compounded semi-annually.

Solution:

Given details are,
Principal (p) = Rs 4096
Rate (r) = 12 ½ % per annum = 25/4% or 12.5/2%
Time (t) = 18 months = (18/12) × 2 = 3 half years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the given values we have, 
= 4096 (1 + 12.5/2×100)³
= 4096 (212.5/200)³
= Rs 4913
∴ Amount is Rs 4913

Question 8. Find the amount and the compound interest on Rs. 8000 for 1 ½ years at 10% per annum, compounded half-yearly.

Solution:

Given details are,
Principal (p) = Rs 8000
Rate (r) = 10 % per annum = 10/2% = 5% (half yearly)
Time (t) = 1 ½ years = (3/2) × 2 = 3 half years
By using the formula,

Substituting the values we have, 
A = P (1 + R/100)ⁿ
= 8000 (1 + 5/100)³
= 8000 (105/100)³
= Rs 9261

Calculating for Compound Interest, we have
∴ CI = Rs 9261 – 8000 = Rs 1261

Question 9. Kamal borrowed Rs. 57600 from LIC against her policy at 12 ½ % per annum to build a house. Find the amount that she pays to the LIC after 1 ½ years if the interest is calculated half-yearly.

Solution:

Given details are,
Principal (p) = Rs 57600
Rate (r) = 12 ½ % per annum = 25/2×2% = 25/4% = 12.5/2% (half yearly)
Time (t) = 1 ½ years = (3/2) × 2 = 3 half years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 57600 (1 + 12.5/2×100)³
= 57600 (212.5/200)³
= Rs 69089.06
∴ Amount is Rs 69089.06

Question 10. Abha purchased a house from Avas Parishad on credit. If the cost of the house is Rs. 64000 and the rate of interest is 5% per annum compounded half-yearly, find the interest paid by Abha after one year and a half.

Solution:

Given details are,
Principal (p) = Rs 64000
Rate (r) = 5 % per annum = 5/2% (half yearly)
Time (t) = 1 ½ years = (3/2) × 2 = 3 half years
By using the formula,
A = P (1 + R/100)ⁿ

Substituting the values we have, 
= 64000 (1 + 5/2×100)³
= 64000 (205/200)³
= Rs 68921

Calculating for Compound Interest, we have
∴ CI = Rs 68921 – 64000 = Rs 4921

Chapter 14 Compound Interest - Exercise 14.2 | Set 2

Conclusion

Understanding compound interest is essential for the making informed financial decisions whether for the saving money or investing. Exercise 14.2 | Set 1 in Chapter 14 of RD Sharma's textbook helps students practice and master the calculations involved in the compound interest. Proficiency in this area will provide a strong foundation for the managing finances effectively and understanding more complex financial concepts.