Complete Guide on How to Solve Compound Interest Problems for NID 2023

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} ᵀ

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.

How to Solve 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.

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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: -

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

How to prepare simple and compound interest for NID 2023?

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 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.

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} ᵀ

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?

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 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?

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/-

Question 14: A sum of money under compound interest doubles itself in 4 years. In how many years will it become 16 times itself?

1. 12 years
2. 16 years 
3. Ten years
4. None of these
5. Eight years

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

• 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

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