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**Simple and Compound Interest For IBPS RRB 2024 Exam:** Simple and Compound Interest is an easy topic that all candidates must have done in the 5th and 6th class. If the candidates understand it well, then it can be a scoring topic. Interest calculation is a fundamental concept in banking and finance, which is essential for various competitive exams like IBPS RRB 2024. In this article, we are providing an in-depth understanding of simple and compound interest, as well as provide practical questions to help you prepare effectively.

## Simple Interest

**Definition of Simple Interest-** Simple Interest (SI) is interest calculated at a fixed interest rate on the principal amount (initial amount of money) for a fixed period. It is straightforward and does not consider the effect of compounding.

**Formula of Simple Interest -:**

The formula for calculating simple interest is:

- P = Principal amount
- R= Rate of interest per annum
- T= Time period

## Compound Interest

**Definition-** Compound interest (CI) is interest paid on the initial principal amount plus all interest from previous periods. This is different from simple interest because in this the interest is not added to the principal to arrive at the next period’s interest.

**Formula**

The formula for calculating compound interest is:

Where,

- A = Amount
- P = Principal
- r = Rate of interest
- n = Number of times interest is compounded per year
- t = Time (in years)

## Practical Question For Simple Interest and Compound Interest

**Question 1:** Vishal deposits Rs. 600000 at ‘2x’% compound interest whereas Raj deposits an amount equal to half of Vishal’s amount at ‘3x’% simple interest. If the sum of their accumulated amounts will become Rs. 1028160 after 2 years, then find the rate of simple interest?

A) 6%

B) 3%

C) 15%

D) 9%

E) None of the above

**Question 2:** A man deposited Rs. ‘x’ in a scheme which offers compound interest at the rate of 10% per annum. If the amount becomes Rs. 21780 and Rs. 23958 at the end of 2^{nd} year and 3^{rd} year respectively, then find the value of ‘x’.

A) Rs. 18500

B) Rs. 17000

C) Rs. 19000

D) Rs. 20000

E) None of these

**Question 3:** Devraj invested some amount at the rate of 12% per annum on simple interest for 2 years. If he had invested the same amount in a scheme offering the same interest rate for 2 years but compounded annually, he would have got Rs. 216 more. Find the amount invested by him.

A) Rs. 20000

B) Rs. 15000

C) Rs. 24000

D) Rs. 30000

E) None of these

**Question 4:** The simple interest earned on an amount of Rs. 2800 at rate of (x + 2)% per annum for 3 years is equal to the simple interest earned on an amount of Rs. 2400 at rate of 7% per annum for 4 years. Find the simple interest earned on Rs. 3200 at rate of 8% per annum after ‘x’ years.

A) Rs. 1280

B) Rs. 1536

C) Rs. 1792

D) Rs. 2048

E) Rs. 2304

**Question 5:** Amit invested Rs. (x + 200) at simple interest rate of 10% per annum for 3 years in scheme 1, and Rs. (x + 600) at simple interest rate of 8% per annum for 2 years in scheme 2. If he obtained interest of Rs. 272 more in scheme 1 than scheme 2, then find the average of the two given amounts.

A) Rs. 2300

B) Rs. 2400

C) Rs. 2500

D) Rs. 2600

E) Rs. 2800

**Question 6:** If the difference between simple interest and compound interest on an amount at the rate of 10% per annum for 2 years is Rs. 82, then find the simple interest earned on the same amount for the rate of 8% per annum for 2 years.

A) Rs. 916

B) Rs. 1056

C) Rs. 1215

D) Rs. 1312

E) Rs. 1580

**Question 7:** Dinesh invested a total sum of Rs. 3200 in scheme A and scheme B in the ratio of 3:x respectively. Scheme A and scheme B is offering a simple interest at the rate of 12% and 8% per annum respectively. If the simple interest earned from scheme A after 10 years is equal to the interest earned from scheme B after 9 years, then find the value of ‘x’.

A) 1

B) 2

C) 3

D) 4

E) 5

**Question 8:** Mr. Singh invested a certain sum of money in a scheme offering simple interest at the rate of 12% p.a. for two years. Mr. Sharma invested Rs. 3000 more than Mr. Singh’s investment in another scheme offering compound interest at the rate of 12% p.a. for two years. Find the average interest earned by Mr. Singh and Mr. Sharma after two years, if the difference between the interests earned by them is Rs. 936.

A) Rs. 3,836

B) Rs. 3,272

C) Rs. 3,624

D) Rs. 3,348

E) None of these

**Question 9:** Rajesh had deposited Rs. 190000 at 7% simple interest for ‘x’ years. If it is known that his accumulated amount was Rs. 243200 in ‘x’ years then find ‘x’.

A) 5

B) 7

C) 2

D) 4

E) None of the above

**Question 10:** Farhan and Amrindar deposit Rs. ‘4x + 300’ at 25% p.a. and Rs. ‘3y + 500’ at 20% p.a., respectively at simple interest. Amrindar deposits the amount after one year of Farhan and after 3 years his interest becomes equivalent to Farhan’s interest. Find x:y.

A) 10:19

B) 7:16

C) 11:23

D) 9:20

E) None of these

**Solution 1: D)**

Amount deposited by Raj = 600000 / 2 = Rs. 300000

According to the question,

600000 × [1 + (2x/100)]^{2} + 300000 × [1 + (3x/100) × 2] = 1028160

60 × [100 + 2x]^{2} + 3000 × [100 + 6x] = 1028160

60 × [10000 + 4x^{2} + 400x] + 300000 + 18000x = 1028160

600000 + 240x^{2} + 24000x + 300000 + 18000x = 1028160

240x^{2} + 42000x – 128160 = 0

x^{2} + 175x – 534 = 0

On solving, x = 3

So, rate of simple interest = 3x = 9%

Hence, option d.

**Solution 2: E)**

According to question,

x × (1.1)^{3} – x × (1.1)^{2} = 23958 – 21780

1.331x – 1.21x = 2178

0.121x = 2178

x = Rs. 18000

Hence, option e.

**Solution 3: B)**

Let the principal amount invested be Rs. ‘x’.

According to question,

x × [(1.12)^{2} – 1] – (x × 12 × 0.02) = 216

0.2544x – 0.24x = 216

0.0144x = 216

x = Rs. 15000

So, the initial amount invested by him = Rs. 15000

Hence, option b.

**Solution 4: B)**

According to question,

(2800 × (x + 2) × 3)/100 = (2400 × 7 × 4)/100

28 × (x + 2) × 3 = 24 × 7 × 4

(x + 2) = 8

x = 6

Therefore, required simple Interest = (3200 × 8 × 6)/100 = Rs. 1536

Hence, option b.

**Solution 5: D)**

According to question,

(x + 200) × 10 × 3 – (x + 600) × 8 × 2 = 272 × 100

30x + 6000 – 16x – 9600 = 27200

14x = 27200 + 3600

14x = 30800

x = 30800/14

x = 2200

So, amount invested by Amit are Rs. 2400 and Rs. 2800.

Therefore, required average = (2400 + 2800)/2 = Rs. 2600

Hence, option d.

**Solution 6: D)**

Let, principal amount be Rs. P.

According to question,

P × [10% + 10% + {(10 × 10)/100}%] – P × 10% × 2 = 82

P [21% – 20%] = 82

P = Rs. 8200

Therefore, required interest = 8200 × 8% × 2 = Rs. 1312

Hence, option d.

**Solution 7: E)**

Amount invested in scheme A = (3/(3 + x)) × 3200 = Rs.9600/(3 + x)

Amount invested in scheme B = Rs. (x/(3 + x)) × 3200 = Rs. 3200x/(3 + x)

According to question,

[9600/ (3 + x)] × 0.12 × 10 = [3200x/ (3 + x)] × 0.08 × 9

2304x = 11520, x = 5

So, the value of ‘x’ is 5.

Hence, option e.

**Solution 8: D)**

Let the amount invested by Mr. Singh be Rs. ‘x’

Interest earned by Mr. Singh after two years = (x × 0.12 × 2) = Rs. 0.24x

Amount invested by Mr. Sharma = Rx. (x + 3000)

Interest earned by Mr. Sharma = (x + 3000) × {(1 + 0.12)^{2} – 1} = (x + 3000) × 0.2544

= Rs. (0.2544x + 763.2)

According to question,

0.2544x + 763.2 – 0.24x = 936

0.0144x = 172.8

x = 12000

So, the interest earned by Mr. Singh = 0.24 × 12000 = Rs. 2,880

Interest earned by Mr. Sharma = 0.2544 × 12000 + 763.2 = 3052.8 + 763.2 = Rs. 3,816

Average interest earned by Mr. Singh and Mr. Sharma = (2880 + 3816) ÷ 2 = Rs. 3,348

Hence, option d.

**Solution 9: D)**

According to the question,

243200 = 190000 + 190000 × 0.07 × x

243200 = 190000 + 13300 × x

53200 = 13300 × x

x = 4

Hence, option d.

**Solution 10: D)**

So, {(4x + 300) × 25 × 4}/100 = {(3y + 500) × 20 × 3}/100

4x + 300 = (9y + 1500)/5

20x + 1500 = 9y + 1500

20x = 9y

x : y = 9 : 20

Hence, option d.

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## Simple and Compound Interest For IBPS RRB Exam FAQ

**What is Simple Interest (SI)?**

Simple Interest is the interest calculated on the principal amount for a certain period at a fixed rate of interest.

**What is Compound Interest (CI)?**

Compound Interest is the interest calculated on the initial principal, which also includes all the accumulated interest from previous periods.

**How do you calculate the total amount (A) using Simple Interest?**

The total amount is calculated as: A= P+SI

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