**Rd sharma Class 8 Chapter 14 Compound Interest Exercise 14.1 Solutions**

This post is created to help all the CBSE Class 8 students for the Solutions of Rd sharma Class 8 Mathematics Book, Chapter 14 Compound Interest Exercise 14.1. Here students can easily find step by step solutions of all the problems for Compound Interest Exercise 14.1. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily.

**Chapter 14 – Compound Interest**

**Compound Interest – Exercise 14.1 all Questions Solution**

**Question no – (1) **

**Solution : **

As per the question,

Principal = 3000 Rs

rate = 5%

n = 2 years

∴ Amount = P(1 + r/100)^n

= 3000 (1 + 5/100)²

= 3000 (100+5/100) ²

= 3000 × 105/100 × 105/1000

= 3307.5

∴ Compound Interest = 3307.5 – 3000.00

= 307.5 Rs.

Therefore, the compound interest will be Rs. 307.5

**Question no – (2) **

**Solution : **

According to the question,

Principal = 400 Rs

rate = 5%

n = 2 years

∴ Amount = p (1 + r/100)^n = 4000 (1 + 5/100)²

= 4000 (100+5/100) ² = 4000 (105/100) ²

= 400 × 105/100 × 105/100 = 4410

∴ Compound Interest,

= 4410 – 4000

= 410

Thus, the compound interest will be 410 Rs.

**Question no – (3) **

**Solution : **

As per the given question,

Principal = 8000 Rs

rate = 15%

n = 3

∴ Amount = p (1 + r/100)^n

= 8000 (1 + 15/100)³

= 8000 (100 + 15/100)³

= 8000 × 105/100 × 105/1000 × 105/100

= 12167 Rs.

∴ Compound Interest,

= 12167 – 8000

= 4167 Rs.

Therefore, the compound interest that Rohit will gets Rs. 4167

**Question no – (4) **

**Solution : **

According to the question,

Principal = 1000 Rs

rate = 8%

n = 1 1/2 = 3/2 years

∴ Amount = p (1 + r/100)^2n

= 1000 (1 + 8/100)^2 3/2

= 1000 (100 + 8/100)³

= 1000 × 108/100 × 108/100 × 108/100

= 1124.86

∴ Compound Interest,

= 1124.86 – 1000

= 124.86 Rs

Therefore, the compound interest on Rs 1000 will be Rs 124.86.

**Question no – (6) **

**Solution : **

According to the question,

Principal = 16000 Rs

rate = 12 1/2% = 25/2%

n = 3 years

∴ Amount = P (1 + r/100)^n

= 16000 (1 + 25/2/100)³

= 16000 (1 + 25/200)³

= 16000 (200 + 25 /200)

= 16000 × 225/200 × 225/200 × 225/200

= 22781.25 Rs

∴ Compound Interest,

= 22781.75 – 16000

= 6781. 25 Rs.

Therefore, the total compound interest payable by Swati is Rs. 6781.25

**Question no – (7) **

**Solution : **

According to the question,

P = 64000 Rs

r = 10%

n = 1 1/2y = 3/2y

∴ A = p (1 + r/100) ^2n

= 64000 (1 + 10/100)^2 2/3

= 64000 (100 + 10/100)³

= 64000 × 100/100 × 110/100 × 100/100

= 78088 Rs

∴ Compound interest = 78088 – 64000

= 10088 Rs

Thus, the compound interest payable by Roma is Rs. 10088

**Question no – (8) **

**Solution : **

As per the question,

Principal = 20000

Rate = r = 18%

Time = n = 2 y

For Simple Interest,

∴ Simple Interest = PRT/100

= 20000 × 18 × 2 /100

= 7200 Rs

Now, For Compound Interest,

Amount = P (1 + r/100)^n

= 2000 (1 + 18/100)²

= 20000 (100 + 18/100)²

= 20000(100 + 18/100)²

= 20000 ×118/100 × 118/100

= 27848 Rs

∴ Compound Interest

= 27848 – 20000

= 7848 Rs

∴ His gain

= 7848 – 7200

= 648 Rs

**Question no – (9) **

**Solution : **

According to the question,

Principal = 800

rate = 20%

n = 9 month = 9/12 years = 3/4 × 4 quarter

∴ Amount = P (1 + r/100)^n

= 8000 (1 + 20/100)³

= 8000 (100 + 20/100)³

= 8000 × 120/100 × 120/100

= 9261 Rs

∴ Compound Interest,

= 9261 – 8000

= 1261 Rs

Therefore, the compound interest on Rs 8000 will be Rs. 1261.

**Question no – (10) **

**Solution : **

As per the given question,

Simple Interest = 200

Rate = r = 10%

n = Time = 2 years

For Simple Interest,

According to question,

Simple Interest = PRT /100

or, P = SI × 100/ RT

= 200 × 100/10 × 2

= 1000 Rs

For Compound Interest,

∴ Amount = P (1 + r/100)

= 1000 (1 + 10/100)²

= 1000 (100 + 10/100)²

= 1000 × 110/100 × 110/100

= 1210 Rs

∴ Compound Interest

= 1210 – 1000

= 210 Rs

Therefore, the compound interest will be Rs. 210

**Question no – (11) **

**Solution : **

As per the given question,

Principal = 64000 Rs

rate =10%

n = 1 year

∴ Compound Interest for quarterly we know that,

∴ Amount = P (1 + r/100)^4n

= 64000 (1 + 10/100)⁴

= 64000 (100 + 10/100)⁴

= 64000 × 110/100 × 110/100 × 110/100 × 110/100

= 70644.03 Rs

∴ Compound Interest,

= 70644.03 – 64000

= 6644.03 Rs

Therefore, the compound interest on Rs 64000 will be Rs 6644.03

**Question no – (12) **

**Solution : **

According to the given question,

Principal = 7500 Rs

rate = 12/4% = 3% [quarterly]

n = 9 month = 9/12 years = 3/4 × 4 quarterly = 3 quarter

∴ Amount = P (1 + r/100)^n = 7500 (1 + 3/100) ³

= 7500 (100 + /100)³

= 7500 × 103/100 v 103/100 × 103/100

= 8195.45 Rs

Therefore, Ramesh will receive Rs 8195.45 after 9 months.

**Question no – (13) **

**Solution : **

As per the given question,

Principal = 9600 Rs

rate = 5 1/2% = 11/2%

n = 3 years

∴ Amount = P (1 + r/100)^n

= 9600 (1 + 11/2/100)³

= 9600 (1 + 11/200)³

= 9600 (200 +11/200)³

= 9600 × 211/100 × 211/200 × 211/200

= 11272.72 Rs

∴ Compound Interest = Amount – Principal

= 1127.72 – 9600

= 1672.72 Rs

Therefore, compound interest Anil will pay after 3 years will be Rs 1672.72

**Question no – (14) **

**Solution :**

According to the question,

Principal = 12000 Rs

rate = 5%

n = 3 years

∴ Amount = P (1 + r/100)³ = 12000(1 + 5/100)³

= 12000 (100 + 5/100)³

= 12000 × 105/100 × 105/100 × 105/100

= 13891.50 Rs

∴ Compound Interest,

= 1389.50 – 12000.00

= 1891.50 Rs

Hence, Surabhi has to pay Rs 1891.50 to the company after 3 years.

**Question no – (15) **

**Solution :**

As per the given question,

Principal = 40000

rate = 7%

n = 3 years

∴ Amount = P(1 + r/100)^n = 4000 (1 + 7/100)³

= 12000 (100 + 7/100)³

= 40000 × 107/100 × 107/100 × 107/100

= 45796 Rs

∴ Compound Interest,

= 45769 – 40000

= 5796 Rs

Therefore, Daljit will pays Rs. 5796 after 2 years.