Complete Guide on How to Solve Compound Interest Problems for NID 2025

Overview: Discover the art of mastering compound interest for NID 2025. This guide breaks down complex concepts into simple strategies, helping you excel in your exam preparation. Dive in and unlock the secrets of financial success!

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Compound Interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. In simple terms, we can say that when you get interested in your invested money and interest in that money.

Simple interest means when you get interested in your principal amount only. But compound interest is the interest on the principal sum and the interest earned.

In this article, you will learn all the tips to solve Compound Interest Questions for NID 2025 and some solved Compound interest questions for NID Entrance Exam 2025.

What is Compound Interest?

Interest is the additional money paid by organisations like banks or post offices on money deposited (kept) with them. Interest is also paid by people when they borrow money. When the interest is calculated on the previous year’s amount, the interest is called compounded or Compound Interest (C.I.).

The formula for finding the amount on compound interest is given by -

Where,

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time (in years)

Alternatively, we can write the formula as given below:

CI = A – P

Where,

A = P[1 +(R/100)]^nt

This formula is also called periodic compounding formula.

How to Solve Compound Interest Questions for NID 2025

Compound Interest is an extension of Simple Interest. If you have understood the topic of simple interest thoroughly, you can easily understand the topic of compound interest and score good marks in the NID entrance exam.

Compound interest keeps on adding the interest generated in the principal amount. So, in compound interest is that the principal keeps on getting updated yearly.

Compound interest is used to calculate appreciation, depreciation of assets, decrease or increase of population, etc.

Some of the significant question types which are asked in simple interest and compound interest are as follows: -

1. Finding Rate/Time/Interest/Principal/Amount In Simple Interest
2. Finding Rate/Time/Interest/Principal/Amount In Compound Interest
3. Questions based on differences between simple and compound interest
4. Questions based on becoming amount 'n' times of itself
5. Questions based on Simple Interest Installments
6. Questions based on Compound interest Installments

Know More: How to Solve Simple Interest Questions for NID 2025

How to Prepare for Simple and Compound Interest Questions for NID 2025

The following are some of the tips that will help enhance your NID exam preparation.

• It would be best if you were well-skilled with the concepts of percentages before coming to this chapter.
• Learning to solve simple and compound interest problems for NID using base 100 and fractions would be best.
• You can avoid formulaic approaches to solve the questions.
• You have to learn some tricks applicable to some specific kinds of problems.
• Try to solve as many problems as you can from diversified sources.
• Take online tests to understand the latest trend of questions.

Know More: Previous year exam analysis for NID entrance exam

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Sample Questions with Solutions for Compound Interest Questions for NID

Question: A bank charges a rate of interest of 10% compounded annually. What is the total amount to be paid on a loan of Rs. 36000 for three years?

Solution:

Given:

Rate of Interest = 10% compounded annually

Principal amount = Rs. 36000

Time = 3 years

To find: the interest amount to be paid in 3 years

Solution : 

Principal amount = 36000

Simple interest for three years

Interest amount = Principal x rate of interest x Time

Interest Amount = 36000 x 10% x 3 years

Interest Amount = 36000 x 10/100 x 3

Interest Amount = 10800

Therefore, the simple interest amount for three years will be Rs. 10800, and each year will be Rs. 3600.

Compound interest for three years 

Amount = {1 + Rate/100} ᵀ

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For finding the compound interest -

We will calculate interest for three years.

10% of 36000 = 3600

Rs. 3600 will be the interest every year. 

10% of 3600 for 2nd-year compound interest, i.e. 360

So, the 2nd year interest is 3600 + 360 = 3960

For the 3rd year, 10% interest on 3600 of the 1st year and 3600 of the 2nd year

i.e. 10% of 7200, i.e. 720.

And 10% interest of 360, i.e. 36

So, the 3rd year interest is 3600 + 720 + 36 = 4356

Compound interest (CI) = 3600 (1st year) + 3960 (2nd year) + 4356 (3rd year) = 11916

Compound interest (CI) = 11916

To find the final amount -

Amount = Principal + Compound Interest

Amount = 36000 + 11916

Amount = 47916

Know More: NID Exam Pattern 2025 Marking Scheme

Question: If P = 10000/-, T = 2 years 6 months, rate of interest = 20% compounded annually. Find Amount.

Solution: 

We will calculate interest for three years.

20% of 10000, i.e. Rs. 2000

Rs. 2000 will be the interest.

20% of 2000 for 2nd-year compound interest, is 400

So, the 2nd year interest is 2000 + 400 = 2400

For the 3rd year, 20% interest on 2000 of 1st year and 2000 of 2nd year,

i.e. 20% of 4000, i.e. 800.

And 20% interest of 400, i.e. 80.

So, we will take interest of 2 years total and half interest of 3rd year 

Compound interest (CI) = 2000 (1st year) + 2400 (2nd year) + 1440 (6 months) = 5840.

Compound interest (CI) = 5840.

Amount = Principal + Compound Interest

Amount = 10000 + 5840

Amount = 15840

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Question: If P = 20,000, Rate of Interest = 3% p.a. Time = 2 years three months, Find Compound interest.

Solution:

3% of 20000, i.e. Rs. 600

Rs. 600 will be the interest every year

3% of 600 for 2nd-year compound interest, is 18

So, the 2nd year interest is 600 + 18 = 618

For the 3rd year, 3% interest on 600 of the 1st year and 600 of the 2nd year,

i.e. 3% of 1200, i.e. 36.

And 3% interest of 18, i.e. 0.54.

So, we will take interest of 2 years total and 1/4th interest of 3rd year

Compound interest (CI) = 600 (1st year) + 618 (2nd year) + 159.135 (3 months) = 1377.135

Compound Interest (CI) = 1377.135

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Question: If P = 7.30 lacs, Rate of Interest = 10% p.a. T = two years and two days. Find Compound Interest.

Solution: 

10% of 7,30,000, i.e. Rs. 73000

Rs. 73000 will be the interest every year

10% of 73000 for 2nd-year compound interest, i.e. 7300

So, the 2nd year interest is 73000 + 7300 = 80300

For the 3rd year, 10% interest on 73000 of the 1st year and 73000 of the 2nd year,

i.e. 10% of 1,46,000, i.e. 14600.

And 10% interest of 7300, i.e. 730.

So, we will take interest of 2 years total and two days interest of 3rd year.

Compound interest (CI) = 73000 (1st year) + 80300 (2nd year) + 484 (2 days) = 1,53,784

Compound Interest (CI) = 1,53,784

Question: If P = 18000, Rate of Interest = 16.66%, Time = 1 year 73 days, Find Compound Interest.

Solution: 

16.66% (1/6) of 18000, i.e. Rs. 3000

Then we will write in the boxes mentioned below

Rs. 3000 will be the interest every year

16.66% (1/6) of 3000 for 2nd-year compound interest, i.e. 500

So, the 2nd year interest is 3000 + 500 = 3500

So, we will take interest of 1 year full and 73 days interest of 2nd year

Compound interest (CI) = 3000 (1st year) + 700 (73 days) = 3700

Compound Interest (CI) = 3700

Question: If P = 10400, Rate of Interest = 5%, Time = 1 year and six weeks, interest compounded annually.

Solution:

5% of 10400, i.e. Rs. 520

Rs. 520 will be the interest every year

5% of 520 for 2nd-year compound interest, i.e. 26

So, the 2nd year interest is 520 + 26 = 546

So, we will take interest of 1 year full and six weeks interest in 2nd year.

Compound interest (CI) = 520 (1st year) + 63 (6 weeks) = 583

Compound Interest (CI) = 583

Know More: Important questions for the NID GAT exam

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Question: The differences between Simple interest and compound interest on a certain sum of money at 5% for two years are Rs. 3. Find the sum.

Solution:

For 2 years, the difference between CI and SI is given by the formula:

Difference = (P * R^2) / (100^2)

Substituting the given values:

3 = (P * 5^2) / (100^2)

Simplifying:

3 = (P * 25) / 10000

Solving for P:

P = (3 * 10000) / 25

P = 1200

Therefore, the sum is Rs. 1200.

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Question: If the difference between Compound interest and simple interest on a certain sum of money at 5% p.a. for three years is Rs. 122. Find the sum.

Solution:

For 3 years, the difference between CI and SI is given by the formula:

Difference = P * (R/100)^2 * (300 + R) / 100

Substituting the given values:

122 = P * (5/100)^2 * (305/100)

Simplifying:

122 = P * (25/10000) * (305/100)

Solving for P:

P = (122 * 10000 * 100) / (25 * 305)

P = 16000

Therefore, the sum is Rs. 16000.

Question: Simple interest on a sum of money for two years is Rs. 480, and Compound interest is Rs. 492. Find the sum and rate of interest.

Solution:

Time = 2 years

Simple interest = Rs. 480

Compound Interest = Rs. 492

To Find the Sum and Rate of Interest.

We have simple interest, i.e. Rs. 480

So, this simple interest is for two years,

So, 240 is the simple interest.

And we have compound interest also, i.e. Rs. 492.

Rate of interest,

=) 240 * R/100 = 12

=) R = 5%

Rate of interest = 5%

Principal amount,

=) P * R/100 = SI of 1 year

=) P * 5/100 = 240

=) P * 1/20 = 240

=) P = 240 * 20

=) P = 4800

So,

Principal amount = Rs. 4800

And the rate of interest = 5%

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Question: A man borrowed Rs.80000 at 10% p.a. compound interest, interest being compounded annually. How small should he have repaid at the end of the first year if he can clear the loan by repaying Rs.55000 at the end of the second year?

1. Rs.38000 
2. Rs.33000
3. Rs.45000
4. Rs.50000
5. Rs.40000

Answer: 1. Rs. 38000

Explanation:

Principal= 80000

Rate of interest = 10 % ‘

after the first-year amount = 88000

10 % rate compounded annually

If we paid 55000 at the end of the 2nd year, we paid 110 % of the amount left after paying particular from the 1st year. CI is always calculated on the previous year's amount.

=55000/110 *  100

= 50000

So that a certain amount is paid after the first year, the remaining amount equals 50000.

i.e. the certain amount paid after 1st year is equal to the

= 88000-50000

= 38000

Question: A specific loan amount, compounded under compound interest annually, earns an interest of Rs.1980 in the second year and Rs.2178 in the third year. How much interest did it make in the first year?

1. Rs.1600
2. Rs.1800
3. Rs.2100 
4. None of these
5. Rs.1900

Answer: 2. Rs. 1800

Explanation: 

Interest in 2nd year = 1980 Rs.

Interest in 3rd year = 2178 Rs.

Difference=2178-1980=198

Rae of interest = (198/1980)*100 

= 10%

If the rate of interest is 10 % compounded annually, then the interest in the second year is 11 %

It means 1980 is 11%, and we have to calculate the first year, i.e. we have to calculate 10 % of p

The interest of 1st year = 1980/11*10

= 180*10

= Rs. 1800/-

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Question: A sum of money is lent at a certain interest rate at compound interest. If instead, the same amount was lent at simple interest, the interest for the first two years reduces by Rs.160 and that for the first three years reduces by Rs.488. Find the sum

• Rs.22000
• Rs.46000
• Rs.52000
• Rs.64000
• Rs.46000

Answer: 4. Rs. 64000

Explanation: 

B is the difference B/w 2 years of interest So B = 160

Difference B/w 3 years of C. I and S.I.

= 3B+C = 488

160*3+C = 8

C is calculated on 8

Rate = 8/160*100 = 5%

A = 160/5*100 = 3200

P = 3200/5*100

P = Rs. 64,000

Key Takeaways

• Compound interest is interest calculated on the initial principal and also on the accumulated interest of previous periods.
• Solve a variety of problems to improve your understanding and speed. Practice quick calculations to save time.
• Understand the concept of effective interest rate: Know how to calculate the equivalent annual interest rate for different compounding frequencies.

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