# Tips to Solve Compound Interest Questions for NID

The 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 words, we can say that when you get interested on your invested money and interest in that money.

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

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 get to know all the tips to solve Compound Interest Questions for NID

## How to Solve Compound Interest Questions for NID?

The Compound Interest is an extension of Simple Interest. If you have understood the topic of simple interest thoroughly then you can easily understand the topic of compound interest as well.

When it comes to understanding compound interest we need to understand that simple interest has an anomaly. The anomaly was that whatever interest was generated was not getting added to the principal because whatever interest is getting generated year after year that interest still stays with the person who has 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 entire 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 the principal keeps on getting updated every year.

The compound interest is not just a concept to be used to solve the questions related to compound interest but also the questions related to appreciation, depreciation of assets, decrease or increase of population, and etc.

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

- Finding Rate/Time/Interest/Principal/Amount In Simple Interest
- Finding Rate/Time/Interest/Principal/Amount In Compound Interest
- Questions-based on differences between simple and compound interest
- Questions based on becoming amount ‘n’ times of itself
- Questions based on Simple Interest Installments
- Questions based on Compound interest Installments

### How to prepare simple and compound interest?

- You should be well skilled with the concepts of percentages before coming to this chapter.
- You should learn to solve the simple interest and compound interest problems using base 100 and fractions.
- 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.

There are some of the questions mentioned below with their solution that will help you to get the tips to solve compound interest questions for NID.

**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 3 years?

**Answer: The total amount to be paid = 47916.**

**Explanation:**

**In this question, we will consider the simple interest and compound interest both because that will help you to understand the difference between them easily.**

Given:

Rate of Interest = 10% compounded annually

Principal Amount = Rs. 36000

Time = 3 years

To find: interest amount to be paid in 3 years

Solution :

Principal amount = 36000

Simple interest for 3 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 3 years will be Rs. 10800 and for each year it will be Rs. 3600.

Compound interest for 3 years

Amount = {1 + Rate/100} ᵀ

We will use the box method to solve this question.

We will calculate interest for 3 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 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 you can see in the box below.

Then for the 3rd year, we will calculate 10% interest on 3600 of 1st year and 3600 of 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 you can see 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 3 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 that you will get every year that’s why we have written 2000 in each year 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 you can see 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 have asked only the interest of 2 years and 6 months.

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

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 3 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 3 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 that you will get every year that’s why we have written 600 in each year 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 1st year and 600 of 2nd year i.e. 3% of 1200 i.e. 36. And 3% interest of 18 i.e. 0.54.

But in the question, they have asked only the interest of 2 years and 3 months.

So, we will take interest of 2 years full 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**

**Question 4: **If P = 7.30 lacs, Rate of Interest = 10% p.a. T = 2 years and 2 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 3 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 you can see in the box below.

Then for the 3rd year, we will calculate 10% interest on 73000 of 1st year and 73000 of 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 2 days.

So, we will take interest of 2 years full and 2 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 2 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 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 you can see 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 6 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 2 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 that you will get every year that’s why we have written 520 in each year 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 you can see in the box below.

But in the question, they have asked only the interest of 1 year and 6 weeks.

So, we will take interest of 1 year full and 6 weeks interest of 2nd year

So,

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

**Compound Interest (CI) = 583**

**Question 7:** If P = 8000, Time = 3 years, Rate of Interest = 1%, 2%, and 3%. Find CI – SI =?

**Answer: Compound Interest – Simple Interest = Rs. 7.248**

**Explanation:**

We will use the box method to solve this question.

We will calculate interest for 3 years.

Given that every year rate of interest changes i.e.

1st-year rate of interest is 1%

2nd-year rate of interest is 2%

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 you can see in the box below.

Then for the 3rd year, we will calculate 3% interest on 80 of 1st year and 160 of 2nd year i.e. 3% of 240 i.e. 7.2 And 3% interest of 1.6 i.e. 0.048.

So, we will take 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 2 years are Rs. 3. Find the sum?

**Answer: Sum = Rs. 1200**

**Explanation:**

In this question, there is no principal amount given so we can’t apply the box method here.

So, here we have to approach differently i.e. we will see the rate of interest.

In the question, it is given the rate of interest is 5% and time is 2 years

Convert 5% interest into fraction i.e. 1/20

Now, look at the time

It is 2 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 now we can apply the box method

We will use the box method to solve this question.

We will calculate interest for 2 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 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 you can see 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 3 years is Rs. 122. Find the sum.

**Answer: Sum = Rs. 16,000**

**Explanation:**

In this question, there is no principal amount given so we can’t apply the box method here.

So, here we have to approach differently i.e. we will see the rate of interest.

In the question, it is given the rate of interest is 5% and time is 3 years

Convert 5% interest into fraction i.e. 1/20

Now, look at the time

It is 3 years given

So, we will cube the fraction part of the interest and the base value of that fraction will be our assumed principal amount.

Let Principal = (20) ³

Principal = 8000

Now we have the principal amount now we can apply the box method

We will use the box method to solve this question.

We will calculate interest for 3 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 that you will get every year that’s why we have written 400 in each year 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 you can see in the box below.

Then for the 3rd year, we will calculate 5% interest on 400 of 1st year and 400 of 2nd year i.e. 5% of 800 i.e. 40 And 5% interest of 20 i.e. 1

As you know, 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 2 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 Sum and Rate of Interest.

We have simple interest i.e. Rs. 480

So, this simple interest is of 2 years. It means that for each 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 SI 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 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, 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 given so we can’t apply the box method here.

So, here we have to approach differently i.e. we will see the rate of interest.

In the question, it is given the rate of interest is 15% and time is 3 years

Convert 15% interest into fraction i.e. 3/20

Now, look at the time

It is 3 years given

So, we will cube the fraction part of the interest and the base value of that fraction will be our assumed principal amount.

Let Principal = (20) ³

Principal = 8000

Now we have the principal amount now we can apply the box method

We will use the box method to solve this question.

We will calculate interest for 3 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 that you will get every year that’s why we have written 1200 in each year 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 you can see in the box below.

Then for the 3rd year, we will calculate 15% interest on 1200 of 1st year and 1200 of 2nd year i.e. 15% of 2400 i.e. 360 And 15% interest of 180 i.e. 27

As you know, 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 the rate of 10% p.a. compound interest, interest being compounded annually. How much amount should he have repaid at the end of the first year, if by repaying Rs.55000 at the end of the second year he can clear the loan?

- Rs.38000
- Rs.33000
- Rs.45000
- Rs.50000
- Rs.40000

**Answer: 1. Rs. 38000**

**Explanation:**

Principal= 80000

Rate of interest = 10 % ‘

after first year amount = 88000

10 % rate compounded annually

If we paid 55000 at the end of the 2nd year it means we paid 110 % of the amount left after paying certain from the 1st year. CI always calculated on the previous year amount.

=55000/110 * 100

= 50000

So that certain amount is paid after the first year then the remaining amount is equal to 50000.

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

= 88000-50000

= 38000

**Question 13**: A certain loan amount, under compound interest, compounded annually earns an interest of Rs.1980 in the second year and Rs.2178 in the third year. How much interest did it earn in the first year?

- Rs.1600
- Rs.1800
- Rs.2100
- None of these
- 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 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?

- 12 years
- 16 years
- 10 years
- None of these
- 8 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 become doubled P become 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 rate of interest 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