Compound Interest Short tricks and Example Questions for SSC Exams

Compound Interest Important Formulas, Tricks And their relevent Questions

Ssc asks Problems on Simple, Compound Interests and Installments. The Weightage of compound intrest in SSC exams is around 1-2 Questions. The questions are very easy to Solve, Scoring and less time consuming. It is important that while solving the questions accuracy must be maintained. For this purpose we have to learn some tricks to improve and keep maintain accuracy during the exam.

What is compound intrest

When money is lended for a certain time period, then the compound amount received from the summation of interest ( calulated on initial amount ) received & the principal amount is considered as the principal amount for the next year.

the interest received is added into the principal & thus, the interest of interest is calculated, this process is called the Compound Interest (CI).

Difference between Annual Rate, Quarterly Rate and Half Yearly Rate

Annual Rate

If Interest on money is calculated for 1 year and added into principal amount is called Annual Interest Rate.

Half Yearly Rate

Interest on money is calculated for two times in a year and added into the principal amount is called Half Yearly Interest Rate.

Note: In these kind of questions
Rate is considered one fourth of given question and time is considered 4 times after doing this question converted into Annual Interest Rate

Quarterly Rate

Interest on money is calculated for four times in a year and added into the principal amount is called Half Yearly Interest Rate.

Note: In these kind of questions
Rate is considered one fourth of given question and time is considered 4 times after doing this question converted into Quarterly Interest Rate.

Formulas and Important Tricks of Compound Interest

Type 1

Standard or Basic rule of compound interest

If the foundation of the house is not strong then the house will not last long.
Standard or Basic rule is also foundation of any lesson of mathematics. We should give it as much importance as tricks.

Compound amount = P × `\left(1+\frac{Rate}{100}\right)^{Time}`

Compound Interest (CI) = P × `\left(1+\frac{Rate}{100}\right)^{Time}` - P

Or
Compound Intrest = Compound Amount - P

Where P = Principal Amount in all questions

Rate = Rate of Interest

Trick 1 Fraction or Ratio Method

Important component of Compound interest is Interest rate. If Interest Rate is convertable into fraction then it makes question more easy. 

Percentage	Fraction Form
100%	1
50%	1/2
33.33	1/3
25%	1/4
16.66%	1/6
14.28%	1/7
12.5%;	1/8
11.11%	1/9
10%	1/10
9.09%	1/11

percentage can be converted into ratio or fraction by dividing the number with a hundred.

Example 

If Principle = 1470rs, Rate of Interest = 14.28% then find Compound intrest ?

Condition 1 when time is 2 years
Solution

Condition 2 when time is 3 years but Principle amound is 10290rs

Solution

Acording to the table

14.28% = `frac{1}7`

Here 7 represents Principle Amound and 1 represents Rate of interest. We all know that compound interest is collectively calucated on initial value and Interest value.

Condition 1 when time is 2 years

Compound interest = 1470 × `frac{8}7×frac{8}7` - 1470

Compound Interest = 450rs


Condition 2 when time is 3 years and Principle amound is 10290rs


Compound interest => 10290 × `frac{8}7×frac{8}7 × frac{8}7` - 10290 = 5070

Trick 2 Tree Method

We usually use Tree method when we have a rate that simply be convertable into fraction. After that we make a imaginary question by comparing original to solve the question.

Let's solve previous question by using Trick no. 2 with two conditions

Condition 1 when time is 2 years 

• Here 49 is calculated by multiplying 7 twice becuase here time is 2 year. We cosider it as a initial value.

• When we jump to the second year we get two number 7 and 1. They are calculated by dividing 7 ( fraction value) from 49 ( Initial value)and and 7 ( 1st year interest) respectively

Lets compare these numbers with previous question numbers

VALUES	Tree method	Fraction method
PRINCIPLE	49(a²)	1470
SI	14(2a)	420
CI	15(2a+1)	450
CI - SI	1	30

Compound Interest = `frac{1470}{49}` ×15 = 450

Condition 2 when time is 3 years and Principle amound is 10290rs

• Here 343 is calculated by multiplying 7 thrice l becuase here time is 3 year. We cosider it as a initial value.

• When we jump to the second year we get two number 49 and 7. They are calculated by dividing 7 ( fraction value) from 343 ( Initial value)and and 49 ( 1st year interest) respectively
• When we jump to the third year we get four numbers 49, 7, 7 and 1. These four numbers are calculated by dividing 7 ( fraction value) from 343 ( Initial value), 49 ( 1st year interest), 49 ( 2nd year interest), 7 ( 2nd year interest) respectively.

Lets compare these numbers with previous question numbers

VALUES	Tree method	Fraction method
PRINCIPLE	343(a³)	10290
SI	147(3a²)	4410
CI	169(3a²+3a+1)	5070
CI - SI	22(3a+1)	660

Compound Interest = `frac{10290}{343}` ×169 = 5070

Trick 3 Compound Interest Rate Method

When we combine two interest rate in single one then the output is called Compound Interest Rate.

Majority of SSC aspirats use this method because of it's less time consumption features.

Formula = ` ( x + y + frac{xy}{100})`

Example

If a 2 year compound interest on a sum at the rate of 5% is 328rs, then what is that amount?


Solution

We have Rate of Intrest = 5 %
Then Compound rate for two years is

Compound rate = `( 5 + 5 + frac{5X5}{100})` = 10.25%

Let Amount = x

Compound Interest = x × `frac{10.25}{100} = 380

Amount = 3200rs


Definitely this method will reduce your some steps of solving Compound Interest questions but it totally depends on Interest rate.

If interest rate is easy to compound then you should definitely choose this method.

Which trick is should I adopt to crack Type 1 question

Although all tricks gives us Right answer but it totally depend on Intrest rate

Some rates make tricks lengthy but on the other hand some rates makes tricks more easier.

Lets find out by solving a question with three approach

Question

At the rate of 5% annual interest on an amount, rs 1261 compound interest collected in 3 years. Find the Initial value ?

For solution click button

Easy approach

Approach

`\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}=\;\frac{8000}{9261}`

Amount = 8000

Explaination

Fraction value of 5% is `\frac{1}{20}` So using fraction method after multiplying 3 times we get initial value 8000 and compound value 9261 and compound intrest is 1261

Easy approach

Approach

3 (400) + 3 (20) + 1 = 1261 a³ = 8000 Explaination

In tree method compound Interest value for three years is set as 3a² + 3a + 1 ( check table ) and Principal valie is set as a³
After comparing values we get 8000 as principal

Moderate approach

Approach

5% and 5 % = 10.25% ( compound interest rate for 2 years )
10.25 % + 5 % = 15.7650% ( compound interest for 3 years)

Explaination

3 years compound interest is 15.765% but actually it is 1261 after comparing this we will get 8000 as a Principal amount

Type 2

In Type 2 questions, some money at CI becomes multiple times like two times, three times.
Then question asks about years in which it becomes x times.

Lets take a example

Some money at CI becomes three times in 2 years. In how many years it will become 9 times ?

Standard or Basic rule of compound interest

Compound amount = P × `\left(1+\frac{Rate}{100}\right)^{Time}`


Let P = x rs
Rate = R%

Then

3x = x × `\left(1+\frac{Rate}{100}\right)^2`

3 = `\left(1+\frac{Rate}{100}\right)^2` ....(1)

9x = x `\left(1+\frac{Rate}{100}\right)^{Time}`

Or

9 = `\left(1+\frac{Rate}{100}\right)^{Time}`

3² = `\left(1+\frac{Rate}{100}\right)^{Time}` .......(2)


Here putting the value of 3 from eq. (1) into eq. (2) -

`\left[\left(1+\frac R{100}\right)^2\right]^2 = \left(1+\frac{Rate}{100}\right)^{Time}`

`\left(1+\frac{Rate}{100}\right)^4 = \left(1+\frac{Rate}{100}\right)^{Time}`

According to the Rule of Power -

When two bases are equal, then their powers are also equal.

T = 4 years.

Trick 1

When the money at CI is Increased in Multiple of n, then ;

Trick : `\left[\frac{1^{st}\;power}{t_1}=\frac{2^{nd}\;power}{t_2}\right]`

3 times or 3¹ in 2 years so, 9 times or 9² in x years

Time =` \frac{power\;of\;2^{nd}}{power\;of\;1^{st}\times t_1`

Time = `frac{2}1×2` = 4 years

Trick 2

We will assume that our initial value is x and in 2 years it will become 3x ( x × 3 )
At the same time in another 2 years it will become 9x ( 3x × 3 )

So the total time is 4 years ( 2yrs + 2yrs)

 Type 3 

In Type 3 questions, money was lended on the condition that it was to be returned in two equal installments at some rate of Compound Interest,

Amount of each installments asks in these questions

Lets take a example

3280 rs landed on condition that it was to be returned in two equal installments at 5% annual rate of CI, then find the Amount of Each Installment ?

Standard or Basic rule of compound interest

Amount of Each Installments =

= 1764

Trick

Ratio method

If the installments is given in two times then we need to take 2 ratio of Rate

In this question the Rate of Interest is 5 % and its fraction value is `frac{1}20`

And the ration will be

21 (21 + 1) : 20

Trick = ` 3280\times\frac{21}{41}\times\frac{21}{20} ` = 1764


Here 41 is calculated by adding 21 and 20 because 3280 refers to 41 in installemt procedure

Type 4 

In Type 3 questions, compound Principle of some years given and we need to find Compound Interest Rate ?


Lets take a example

Some money at CI becomes rs 500 in 2 years and rs 550 in 3 years, then what is the Rate of Compound Interest?

Standard or Basic rule of compound interest

Compound Amount = P × `\left(1+\frac{Rate}{100}\right)^{Time}`

Compound of 2 years = rs 500
Compound of 3 years = rs 550

Let Initial value = x

Then

R = 10%

Trick

Rate = `\frac{50}{500}\times100` = 10%



These 4 types of questions is usually asks in SSC Exams mostly in SSC CGL and SSC CHSL.

We can easily solve all these questions with the help of standard formulas anf trick.

So, practice as much as possible to reduce your time in SSC exams and gain maximum marks. For more guidance and tricks, keep on visiting us regularly.