# Class 8 RD Sharma Solutions – Chapter 14 Compound Interest – Exercise 14.1

**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 1210Compound 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 11272.71Compound 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 13891.5Compound 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 45796Compound Interest(CI)= A – P = 45796 – 40000 =

Rs 579