Updated On : November 15, 2022
What to expect from this article: This article is all about Compound Interest and how to solve the questions related to compound interest. We have discussed all the tips and tricks which will help you to score good marks in the NID entrance exam.
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.
The formula of compound interest is:
A = {1 + R/100} áµ€
Here T = Time
A = Amount
P = Principal
R = Rate of Interest
A = Amount = Principal + Compound Interest
In this article, you will learn all the tips to solve Compound Interest Questions for NID 2023 and some solved Compound interest questions for NID 2023.
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.
When understanding compound interest, we must understand that simple interest has an anomaly.
The anomaly was that whatever interest was generated was not added to the principal because whatever interest is generated year after year, that interest still stays with the person who borrowed the money.
Download Free Practice Question Papers for NID Exam by CreativeEdge
And he is not returning you the money each after each; he will return you the money when the entire amount is accumulated, and after the whole duration, finally, when he returns you the amount in that amount, the principal and interest amount is returned to you. This happens in simple interest.
And what compound interest tells us is that it keeps on adding the interest generated in the principal amount. So, what happens in compound interest is that the principal keeps on getting updated yearly.
Compound interest is not just a concept used to solve the questions related to compound interest but also inquiries related to 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: -
The following are some of the tips that will help enhance your NID exam preparation.
With their solution, some of the questions mentioned below will help you get tips to solve compound interest questions for NID.
Read more: Previous year exam analysis for NID entrance exam
Question 1: 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?
Answer: The total amount to be paid = is 47916.
Explanation:
In this question, we will consider simple and compound interests because that will help you understand the difference between them easily.
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} áµ€
Read more: Important questions with answers for the NID CAT exam
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 10% of 36000, i.e. Rs. 3600
Then we will write in the boxes mentioned below
Rs. 3600 will be the interest that you will get every year. That's why we have written 3600 in each year's box.
Now, we will calculate 10% of 3600 for 2nd-year compound interest, i.e. 360
So, the 2nd year interest is 3600 + 360 = 3960, as shown in the box below.
Then for the 3rd year, we will calculate 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, as shown in the box below.
So,
Compound interest (CI) = 3600 (1st year) + 3960 (2nd year) + 4356 (3rd year) = 11916
Compound interest (CI) = 11916
Amount = Principal + Compound Interest
Amount = 36000 + 11916
Amount = 47916
Question 2: If P = 10000/-, T = 2 years 6 months, rate of interest = 20% compounded annually. Find Amount.
Answer: Amount = Rs. 15840
Explanation:
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 20% of 10000, i.e. Rs. 2000
Then we will write in the boxes mentioned below
Rs. 2000 will be the interest you will get every year, which is why we have written 2000 in each year's box.
Now, we will calculate 20% of 2000 for 2nd-year compound interest, i.e. 400
So, the 2nd year interest is 2000 + 400 = 2400, as shown in the box below.
Then for the 3rd year, we will calculate 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.
But in the question, they only asked for the interest of 2 years and six months.
So, we will take interest of 2 years total and half interest of 3rd year
Read more: Best study timetable to enhance your NID preparation
So,
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
Question 3: If P = 20,000, Rate of Interest = 3% p.a. Time = 2 years three months, Find Compound interest.
Answer: Compound Interest (CI) = Rs. 1377.135.
Explanation:
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 3% of 20000, i.e. Rs. 600
Then we will write in the boxes mentioned below
Rs. 600 will be the interest you will get every year, which is why we have written 600 in each year's box.
Now, we will calculate 3% of 600 for 2nd-year compound interest, i.e. 18
So, the 2nd year interest is 600 + 18 = 618, as you can see in the box below.
Then for the 3rd year, we will calculate 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.
But in the question, they only asked for the interest of 2 years and three months.
So, we will take interest of 2 years total and 1/4th interest of 3rd year
So,
Compound interest (CI) = 600 (1st year) + 618 (2nd year) + 159.135 (3 months) = 1377.135
Compound Interest (CI) = 1377.135
Read more: Important questions for the NID CAT exam
Question 4: If P = 7.30 lacs, Rate of Interest = 10% p.a. T = two years and two days. Find Compound Interest.
Answer: Compound Interest (CI) = Rs. 1,53,784.
Explanation:
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 10% of 7,30,000, i.e. Rs. 73000
Then we will write in the boxes mentioned below
Rs. 73000 will be the interest that you will get every year. That's why we have written 73000 in each year box.
Now, we will calculate 10% of 73000 for 2nd-year compound interest, i.e. 7300
So, the 2nd year interest is 73000 + 7300 = 80300, as shown in the box below.
Then for the 3rd year, we will calculate 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.
But in the question, they have asked only the interest of 2 years and two days.
So, we will take interest of 2 years total and two days interest of 3rd year.
So,
Compound interest (CI) = 73000 (1st year) + 80300 (2nd year) + 484 (2 days) = 1,53,784
Compound Interest (CI) = 1,53,784
Question 5: If P = 18000, Rate of Interest = 16.66%, Time = 1 year 73 days, Find Compound Interest.
Answer: Compound Interest (CI) = Rs. 3700
Explanation:
We will use the box method to solve this question.
We will calculate interest for two years.
We will calculate 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 that you will get every year. That's why we have written 3000 in each year's box.
Now, we will calculate 16.66% (1/6) of 3000 for 2nd-year compound interest, i.e. 500
So, the 2nd year interest is 3000 + 500 = 3500, as shown in the box below.
But in the question, they have asked only the interest of 1 year and 73 days.
So, we will take interest of 1 year full and 73 days interest of 2nd year
So,
Compound interest (CI) = 3000 (1st year) + 700 (73 days) = 3700
Compound Interest (CI) = 3700
Question 6: If P = 10400, Rate of Interest = 5%, Time = 1 year and six weeks, interest compounded annually.
Answer: Compound Interest (CI) = Rs. 583
Explanation:
We will use the box method to solve this question.
We will calculate interest for two years.
We will calculate 5% of 10400, i.e. Rs. 520
Then we will write in the boxes mentioned below
Rs. 520 will be the interest you will get every year, and that's why we have written 520 in each year's box.
Now, we will calculate 5% of 520 for 2nd-year compound interest, i.e. 26
So, the 2nd year interest is 520 + 26 = 546, as shown in the box below.
But in the question, they have asked only the interest of 1 year and six weeks.
So, we will take interest of 1 year full and six weeks interest in 2nd year.
So,
Compound interest (CI) = 520 (1st year) + 63 (6 weeks) = 583
Compound Interest (CI) = 583
Read more: Important questions for the NID GAT exam
Question 7: If P = 8000, Time = 3 years, Rate of Interest = 1%, 2%, and 3%. Find CI – S.I. =?
Answer: Compound Interest – Simple Interest = Rs. 7.248
Explanation:
We will use the box method to solve this question.
We will calculate interest for three years.
Given that every year rate of interest changes i.e.
1st-year rate of interest is 1%
The 2nd-year rate of interest is 2%
The 3rd-year rate of interest is 3%
To find: Compound Interest – Simple Interest
Let x be the simple interest of all year
Let y be the compound interest of 2nd and 3rd year
Let z be the compound interest of 3rd year
Now see below
Compound interest = x + x + y + x + 2y + z
Compound interest = 3x + 2y + z
Simple Interest = x + x + x
Simple Interest = 3x
Compound Interest – Simple Interest = 3x + 2y + z – 3x
Compound Interest – Simple Interest = 2y + z ----- equation 1
Equation 1 shows the difference between Compound Interest and Simple Interest is always written on the box. Please analyze equation 1 and the 3rd year box so you will understand everything.
We will calculate 1% of 8000, i.e. Rs. 80
Then we will write in the boxes mentioned below
Rs. 80 will be the interest of 1st year
We will calculate 2% of 8000, i.e. Rs. 160
Rs. 160 will be the interest of 2nd year
We will calculate 3% of 8000, i.e. Rs. 2400
Rs. 240 will be the interest of 3rd year
Now, we will calculate 2% of 80 for 2nd-year compound interest, i.e. 1.6
So, the 2nd year interest is 160 + 1.6 = 161.6, as shown in the box below.
Then for the 3rd year, we will calculate 3% interest on 80 of 1st year and 160 on 2nd year, i.e. 3% of 240, i.e. 7.2, And 3% interest on 1.6, i.e. 0.048.
So, we will take an interest in 3rd year
And as you have analyzed above that
Compound Interest – Simple Interest = 2y + z
So,
Compound Interest – Simple Interest = 7.2 + 0.048
Compound Interest – Simple Interest = 7.248
Question 8: 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.
Answer: Sum = Rs. 1200
Explanation:
In this question, there is no principal amount, so we can't apply the box method here.
So, here we have to approach differently, i.e. we will see the interest rate.
In the question, it is given the rate of interest is 5% and Time t is two years.
Convert 5% interest into a fraction, i.e. 1/20
Now, look at the Time
It is two years, given
So, we will square the fraction part of the interest, and the base value of that fraction will be our assumed principal amount.
Let Principal = (20) ²
Principal = 400
Now we have the principal amount; we can apply the box method
We will use the box method to solve this question.
We will calculate interest for two years.
We will calculate 5% of 400, i.e. Rs. 20
Then we will write in the boxes mentioned below
Rs. 20 will be the interest that you will get every year. That's why we have written 20 in each year's box.
Now, we will calculate 5% of 20 for 2nd-year compound interest, i.e. 1
So, the 2nd year interest is 20 + 1 = 21, as shown in the box below.
As you know, the difference between Compound Interest and Simple Interest of 2 years is Y.
So,
Here Y = 1
And 1 = Rs. 3 (given in question)
We have to find the actual principal
So, if 1 unit = Rs. 3
Then, 400 units = Rs. 3 * 400
i.e. Actual Principal or Sum = Rs. 1200
Question 9: 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.
Answer: Sum = Rs. 16,000
Explanation:
In this question, there is no principal amount, so we can't apply the box method here.
So, here we have to approach differently, i.e. we will see the interest rate.
In the question, it is given the rate of interest is 5% and Time t is three years.
Convert 5% interest into a fraction, i.e. 1/20
Now, look at the Time
It is three years, given
So, we will cube the fraction part of the interest, and that fraction's base value will be our assumed principal amount.
Let Principal = (20) ³
Principal = 8000
Now we have the principal amount; we can apply the box method
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 5% of 8000, i.e. Rs. 400
Then we will write in the boxes mentioned below
Rs. 400 will be the interest you will get every year. That's why we have written 400 in each year's box.
Now, we will calculate 5% of 400 for 2nd-year compound interest, i.e. 20
So, the 2nd year interest is 400 + 20 = 420, as shown in the box below.
Then for the 3rd year, we will calculate 5% interest on 400 of 1st year and 400 on the 2nd year, i.e. 5% of 800, i.e. 40, And 5% interest on 20, i.e. 1
The difference between Compound Interest and Simple Interest of 3 years is 2Y + Z.
So,
Here 2Y + Z = 61
And 61 = Rs. 122 (given in question)
We have to find the actual principal
So, if 1 unit = Rs. 2
Then, 8000 units = Rs. 2 * 8000
i.e. Actual Principal or Sum = Rs. 16000
Question 10: 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.
Answer: Principal amount = Rs. 4800
Rate of interest = 5%
Explanation:
Given: 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, meaning that year, you are getting Rs. 240 as simple interest.
And we have compound interest also, i.e. Rs. 492.
Now see the box method
So as you see, if you have both S.I. and CI, then
We can find the rate of interest like this:
=) 240 * R/100 = 12
=) R = 5%
Rate of interest = 5%
When we find the principal amount, the formula is
=) 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%
Question 11: Principal =? Time = 3 years, Rate of Interest = 15%, Compound interest – Simple interest = Rs. 1701.
Answer: Sum = Rs. 24000
Explanation:
In this question, there is no principal amount, so we can't apply the box method here.
So, here we have to approach differently, i.e. we will see the interest rate.
In the question, it is given the rate of interest is 15% and Time t is three years.
Convert 15% interest into a fraction, i.e. 3/20
Now, look at the Time
It is three years, given
So, we will cube the fraction part of the interest, and that fraction's base value will be our assumed principal amount.
Let Principal = (20) ³
Principal = 8000
Now we have the principal amount; we can apply the box method
We will use the box method to solve this question.
We will calculate interest for three years.
We will calculate 15% of 8000, i.e. Rs. 1200
Then we will write in the boxes mentioned below
Rs. 1200 will be the interest you will get every year, which is why we have written 1200 in each year's box.
Now, we will calculate 15% of 1200 for 2nd-year compound interest, i.e. 180
So, the 2nd year interest is 1200 + 180 = 1380, as shown in the box below.
Then for the 3rd year, we will calculate 15% interest on 1200 of 1st year and 1200 on 2nd year, i.e. 15% of 2400, i.e. 360, And 15% interest on 180, i.e. 27
The difference between Compound Interest and Simple Interest of 3 years is 2Y + Z.
So,
Here 2Y + Z = 1701
And 567 = Rs. 1701 (given in question)
We have to find the actual principal
So, if 1 unit = Rs. 3
Then, 8000 units = Rs. 3 * 8000
i.e. Actual Principal or Sum = Rs. 24000
Question 12: 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?
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 13: 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?
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/-
Question 14: A sum of money under compound interest doubles itself in 4 years. In how many years will it become 16 times itself?
Answer: 2. 16 years
Explanation:
If Time is constant, then the ratio of principal and amount is always constant in compound interest.
in 4 years sum becomes doubled, P becomes 2P
p _____4 years ____2p___4years _____8p ___4 years ____ 16
4+4+4+4= 16 years
Question 15: 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
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
Creative Edge, a TopRankers initiative, is one of the top online NID coaching centres. Here, we make your NID preparation more fun and easier to process. We help you to shape your skills and nourish your qualities to excel in the exam.
Learn more: NID Online Coaching
Download Your Free NID Prep Material
Fill your details
Frequently Asked Questions
How long does it take for NID Exam Preparation?
Which book is best for NID preparation?
Can I crack NID Exam in 3 months?
How Can I manage time in NID Exam?
Is NID exam easy?
How much time should I keep aside for revision in the NID Exam Preparation plan?