**Rd sharma Class 8 Chapter 14 Compound Interest Exercise 14.2 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 14.2. Here students can easily find step by step solutions of all the problems for Compound Interest Exercise 14.2. 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 14.2 all Questions Solution**

**Question no – (1) **

**Solution : **

**(i)** As per the given question,

Principal = 3000

rate = 5%

n = 2 years

∴ Amount = p (1 + 5/100)^n = 3000 (100 + 5/100)²

= 3000 × 105/100 × 105/100

= 3307.5 Rs.

∴ Compound Interest,

= 3307.5 – 3000

= 307.5 Rs.

Therefore, the amount will be 3307.5 Rs and compound Interest will be 307.5 Rs.

**(ii)** As per the question,

Principal = 3000 Rs

rate = 18%

n = 2 years

∴ Amount = P (1 + r/100)^n = 3000 (1 + 18/100)²

= 3000 × 118/100 × 18/100

= 4177.2 Rs.

∴ Compound Interest,

= 4177.2 – 3000

= 1177.2 Rs.

Therefore, the amount will be 4177.2 Rs and compound Interest will be 1177.2 Rs.

**(iii)** According to the question,

Principal = 5000 Rs.

rate = 10%

n = 2y

∴ Amount = P (1 + r/100)^n = 5000 (1 + 10/100)²

= 5000 (100 + 10/100)²

= 5000 × 110/100 × 110/100

= 6050 Rs.

∴ Compound Interest,

= 6050 – 5000 Rs.

= 1050 Rs.

Therefore, the amount will be 6050 Rs and compound Interest will be 1050 Rs.

**(iv)** As per the given question,

Principal = 2000 Rs

rate = 4%

n = 3

∴ Amount = P (1 + r/100)^n = 2000 (1 + 4/100)³

= 2000 × (100 + 4/100)³

= 2000 × 104/100 × 104/100 × 104/10

= 2249.68 Rs

∴ Compound Interest,

= 2249.68 – 2000

= 249 .68 Rs

Therefore, the amount will be 2249.68 Rs and compound Interest will be 249 .68 Rs.

**(v)** In then given question,

Principal = 12800

rate = 7 1/2% = 7.5%

n = 3 years

∴ Amount = P (1 + r/100)^n

= 12800 (1+7.5/100)³

= 12800 (1.075)³

= 15901.40 Rs

∴ Compound Interest,

= 15901.40 – 12800.00

= 3101.40 Rs

Therefore, the amount will be 15901.40 Rs and compound Interest will be 3101.40 Rs.

**(vi)** According to the given question,

Principal = 10000

rate = 20%

n = 2 year

∴ Amount = P (1 + r/100)^2n = 10000 (1 + 20/200)⁴

= 10000 (10 + 2/20) = 10000(12/20)⁴

= 10000 × 12/20 × 12/20

= 14641 Rs

∴ Compound Interest,

= 14641 – 10000

= 4641 Rs

Therefore, the amount will be 14641 Rs and compound Interest will be 4641 Rs.

**(vii)** As per the given question,

Principal = 160000 Rs

rate = 10 paise per rupee per annum compounded half-yearly.

n = 2 years

∴ Amount = P (1 + r/100)^2n = 1000 (1 + 10/100)⁴

= 10000 (100 + 10/100)⁴

= 10000 (110/100) ⁴

= 10000 × 11 × 11 × 11 × 11/10 × 10 × 10 × 10

= 19448.10 Rs

∴ Compound Interest,

= 19448.10 – 16000

= 3448.10 Rs

Therefore, the amount will be 19448.10 Rs and compound Interest will be 3448.10 Rs.

**Question no – (2) **

**Solution : **

According to the question,

Principal = 2400 Rs

rate = 20%

n = 3 years

∴ Amount = P (1 + r/10)^n = 2400 (1 + 20/100)³

= 2400 (100+20/100)³

= 2400 × 120/100 × 120 × 100 × 120/100

= 4147.20 Rs

Therefore, the required amount will be Rs 4147.20.

**Question no – (3) **

**Solution : **

As per the given question,

Principal = 16000 Rs

rate = 12 1/2% = 25/2 = 12.5%

n = 3 years

∴ Amount = P (1 + r/1000)^n

= 16000 (1 + 72.5/100) ³

= 16000 (1.125)³

= 22781.25 Rs

Hence, the amount which is payable Rasheed to Rahman will be 22781.25 Rs.

**Question no – (4) **

**Solution : **

In the given question,

Principal = 1000

rate = 10%

n = 2 years

∴ Amount = P (1 + r/100)^n

= 1000 (1 + 10/100)²

= 1000 (1.1)²

= 1210 Rs

Therefore, the amount that Meera has to pay back will be 1210 Rs.

**Question no – (6) **

**Solution :**

As per the given question,

Principal = 16000 Rs

Rate = r = 17 1/2% = 17.5%

Time = n = 2 years

For Simple Interest,

S.I. = PRT/100 = 1600 × 10 × 2/100

= 5600 Rs

For Compound Interest,

∴ Amount = P (1 + r/100)^n

= 1600 (1 + 17.5/100) ²

= 16000 (1.175)²

= 22090 Rs

∴ Compound Interest,

= 22090 – 16000

= 6090 Rs

∴ His gain at end of 2 years,

= 6090 – 5600

= 490 Rs

Therefore, Amit will gain Rs 490 at the end of 2 years.

**Question no – (7) **

**Solution :**

According to the given question,

Principal = 4096 Rs

rate = 12 1/2% = 25/2 = 12.5%

n = 18 months = 18/12 = 3/2 years

∴ Amount = P (1 + r/200)^2n

= 4096 (1 + 12.5/200)^2 2/3

= 4096 (1.0625)³

= 4913 Rs

Therefore, the required amount will be 4913 Rs.

**Question no – (8) **

**Solution :**

As per the question,

Principal = 8000 Rs

rate = 10%

n = 1 1/2 = 2/3

∴ Amount = P (1 + r/200)^2n

= 8000 (1 + 10/200)^2 3/2

= 8000 (1.05)³

= 9261 Rs

∴ Compound Interest,

= 9261 – 8000 Rs

= 1261 Rs

Therefore, the amount will be 9261 and comp[und interest will be 1261 Rs.

**Question no – (9) **

**Solution :**

As per the given question,

Principal = 57600 Rs

rate = 12 1/2% = 12.5%

n = 1 1/2 = 3/2

∴ Amount = P (1 + r/200)^2n

= 5770 (1 + 12.5/200)^2 3/2

= 57600 (1.0625)³

= 69089.06 Rs

Hence, the amount that she pays will be 69089.06 Rs.

**Question no – (10) **

**Solution :**

According to the given question,

Principal = 64000 Rs

rate = 5%

n = 1 1/2 = 3/2

∴ Amount = P (1 + r/200)

= 6400 (1 + 5/200)^2.3/2

= 6400 (1 + 5/200)³

= 6400 (1.025)³

= 68921 Rs

∴ Compound Interest,

= 68921 – 64000

= 4921 Rs

Therefore, Abha will pay 4921 Rs interest after one year and a half.

**Question no – (11) **

**Solution :**

According to the given question,

Principal = 10000 Rs

rate = 20%

n = 2 years

∴ For compounded annually,

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

= 1000 (1 + 20/100)²

= 10000 (1.2)²

= 14400 Rs

Now, for compounded half-yearly,

Amount = P (1 + r/200)^2n = 1000 (1 + 20/200) ^2.2

= 10000 (1.1)⁴

= 14641 Rs

∴ Difference,

= 14641 – 14400

= 241 Rs

**Question no – (12) **

**Solution :**

As per the given question,

Given in the question,

Principal = 245760 Rs

Rate = 12.5%

n = 2 years

∴ For compounded annually,

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

= 245760 (1 + 12.5/100)²

= 245760 (1.2656)

= 311040 Rs

Now, for compounded semi annually,

Amount = P (1 + r/200)^2n

= 245760 (1 + 12.5/200)^2.2

= 245760 (1.0625)⁴

= 313203.75 Rs

∴ His gain after 2 years,

= 313203.75 – 311040.00

= 2163.75 Rs.

**Question no – (13) **

**Solution :**

From the question,

Principal = 8192 Rs

rate = 12 1/2 = 12.5%

n = 18 months = 18/12= 3/2 years

∴ Amount = P (1 + r/200)^2n

= 8192 (1 + 12.5/200)^2 3/2

= 8192 (1.0625)³

= 9826 Rs

Therefore, the amount that David would receive will be 9826 Rs.

**Question no – (17) **

**Solution : **

According to the question,

Principal = 15625 Rs

rate = 16%

n = 2 1/4 years

∴ Amount = P (1 + r/100)² (1+ r/200)

= 15625 (1 + 16/100)² (1 + 16/200)

= 15625 × (1.16)² × (1.04)

= 21866 Rs.

Therefore, payment Ramu have to make will be Rs. 21866

**Question no – (20) **

**Solution : **

Let, the sum is = P

rate = 20%

n = 2 years

For compounded yearly,

A₁ = P (1 + r/100) ^n

= P (1 + 20/100)²

= P (1.20)²

= 1.44P

Compound Interest,

= 1.44p – P

= 0.44p

Now, for compounded half-yearly,

A₂ = P (1 + r/200) ^2n

= P (1 + 20/200)^2×2

= P (1.1) ⁴

= 1.4641p

Compound Interest,

= 1.4641p – P

= 0.4641P

According to question,

0.4641P – 0.44P = 482

or, 0.0241P = 482

or, P = 482/0.024

p P = 20,000 Rs

Therefore, the required sum will be Rs. 20,000

**Question no – (21) **

**Solution : **

As per the given question,

Simple Interest = 5200 Rs.

R = r = 6 1/2% = 6.5%

T = n = 2 years

For Simple Interest,

S.I = PRT/100

or, Principal = Simple Interest × 100/R.T

= 5200 × 100/6.5 × 2

= 40000 Rs.

Now, for Compound Interest,

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

= 4000 (1 + 6.5/100)²

= 40000 (1.06)²

= 45369 Rs.

∴ Compound Interest,

= 45369 – 40000

= 5369 Rs.

Therefore, the compound interest will be 5369 Rs.

**Question no – (22) **

**Solution : **

According to the question,

Simple Interest = 1200 Rs

R = r = 5%

T = n = 3 y

For Simple Interest,

Simple Interest = PRT/100

or, P = Simple Interest × 100/R.T

= 1200 × 100/ 5 × 3

= 8000

Now for Compound Interest,

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

= 8000 (1 + 5/100)³

= 8000 (1.05)³

= 9261

∴ Compound Interest,

= 9261 – 8000

= 1261

Therefore, the compound interest is Rs. 1261