# Simple Interest and Compound Interest for SSC & Railways Exams

By : Sachin Awasthi

Updated : Nov 6, 2020, 13:58

Simple Interest and Compound Interest questions are most common in Government exams such as SSC CGL, SSC CHLS and other Railway Exams. Simple Interest and Compound Interest topic should not be skipped as it is highly scoring and if prepared in the correct manner can help you improve your score tremendously.

Understand all the details about Simple Interest and Compound Interest topic, the best way to prepare Simple Interest and Compound Interest questions, best books to refer to, important tips and more. This article shows how to use these correct formula and tricks for calculating interest. . Knowledge of computing simple and compound interest will be useful for those appearing for the following exams:

• SSC CHSL Tier I
• SSC CGL Tier I (Preliminary)
• RRB Mathematics Section

## Important Simple Interest and Compound Interest Topics

When you borrow money from a bank (or any other lender), the bank needs to make a profit from the act of lending to sustain itself. And so it charges a service fee. This fee charged by the bank is called interest.

A borrowed amount is usually repaid in monthly or yearly instalments. And every month/year the principal amount is returned along with interest to the lender. There are two kinds of interest that are calculated: simple and compound.

Simple Interest: If interest is being calculated on the principal amount borrowed, it is called simple interest.

Compound Interest: If the interest is being calculated on the principal amount + the accumulated interest amount, it is called compound interest.

### Simple Interest and Compound Interest Formulas

 Simple Interest Formulas Compound Interest Formulas SI = (P x R x T) / 100SI - Simple InterestP - Principal AmountR - Rate of Interest (in %)T - Time period for which money is borrowed (no. of years)A = P + SIA - The total amount to be paid at the end of the lending period. CI = A - PWhen interest is compounded every year, the following formula is used.A = P (1 + R/100)tA = Total amount to the paidP = Principal AmountR = Rate of Interestt = Time period for which money is borrowed.When the interest is compounded more than once a year the following formula is used:A = P (1 + (R/n) /100)ntn - number of times a year interest is calculatednt - number of times interest is calculated x time period for which money is borrowed

### Sample Problems for Simple Interest

 No Difficulty Level Question, Answer and Solution 1 Low What amount will be paid when simple interest is calculated on a principal sum of 8600 at the rate of 7% for 4 years? Answer: 11008SolutionSI = P x N x R / 100 = 8600 x 7 x 4 / 100 = 2408A = P + SI = 8600 + 2408 = 11008 2 Medium A sum of 500 becomes 530 when simple interest is calculated for a period of 3 years. If the simple interest is increased by 5% what Amount will be calculated at the end of 3 years. Answer: 605SolutionA = P + SI530 = 500 + SISI = 30SI = P x N x R / 10030 = 500 x 3 x R / 100R = 2If R is increased by 5%, R = 7%Hence SI = 500 x 7 x 3 / 100 = 105A = P + SI = 500 + 105 = 605 3 High If a sum of money gets doubled when simple interest is calculated over a period of 5 years, what is the rate at which interest has been calculated? Answer: 20%SolutionA = SI + P2x = x + SISI = xSI = P x N x R / 100x = x x 5 x R / 100R = 20%

### Sample Problems for Compound Interest

 No Difficulty Level Question, Answer and Solution 1 Low A hawker lends Rs. 2500 at the rate of 2% compound interest. How much extra money will he have earned at the end of 2 years. Answer: Rs. 101SolutionA = P (1 + R/100 )tA = 2500 (1 + 2/100 )2A = 2500 (102/100)]2A = 2500 x (1.02)2A = 2500 x 1.0404A = 2601CI = A - P = 2601 - 2500 = 101 2 Medium In how many years will a principal amount of Rs. 1000 become Rs. 1728 when compounded annually at the rate of 20% per annum. Answer: 3 yearsSolutionA = P (1 +R/100)t1728 = 1000 (1 + 20/100)t1728 = 1000 (120/100)t1728 / 1000 = (12/10)tt = 3 3 High What will the compound interest for a period of 6 months calculated quarterly at the rate of 20% on a principal amount of Rs. 32,000 be? Answer: Rs. 4,280SolutionA = P ( 1 + (r/n)/100 )tnCI + P = P ( 1 + ( r/n) /100 )tnCI + 32000 = 32000 ( 1 + (20/4) /100)4 x (6/12)CI + 32000 = 32000 (1 + 5/100)4 x ½CI + 32000 = 32000 ( 105/100)2CI + 32000 = 32000 x 105/100 x 105/100CI + 32000 = 32000 x 21/20 x 21/20CI + 32000 = 36280CI = 4280

### Tips to Solve/ Prepare for Simple and Compound Interest Questions

• Short Cuts

When beginning preparation for exams, it is best that students understand the basics very well and solve all the questions on their own by using the basic formulas and natural logic. Once the students have understood the fundamentals, they can then use shortcuts that they will develop on their own, or from other sources.

If students are not good at the basic level, somewhere, they will rely on the limited set of questions they have been exposed to and will not be able to solve a question that even slightly deviates from the questions they know.

In any case, here are some quick ways to solve questions:

Simple Interest

1. The total amount payable including simple interest is A = P + SI.

SI = (P x T x R) / 100

To directly calculate A use the formula P + (P x T x R)/100 instead of doing it in two steps.

1. If a sum becomes 5 times the original amount over a period of 10 years the rate of interest can be calculated thus:

R = 100 (5-1) / 10

Compound Interest

1. CI = P [ 1 + R/100]t – P
2. When compound interest is calculated every six months R = R / 2 and t = 2t.
3. When the rates of interest are different for, say, 3 consecutive years, the total amount including interest is calculated in this way: P ((1 + r1)/100)((1 + r2)/100) ((1 + r3)/100)

There are 2 basic formulas for calculating the SI/CI and the total amount to be paid, including interest. For both types of interest, one needs the rate of interest, the time period and the principal amount. Once you’ll start solving questions, you will become used to the direct formulas for calculating the rate of interest, time and the principal amount. This will be a huge time saver in the exam.

Read the question carefully before you rush to answer it. Take more time to read the question and less to work it out. With good practice, once you’ve understood the question, solving it will be quick.

### Importance of Simple and Compound Interest Section in Government Exams

• In the SSC CGL Tier 1 exam and the SSC CHSL exam, the quantitative sections carry 200 marks and 50 marks respectively and 1-2 questions in this section are simple and compound interest questions.
• These are questions of moderate difficulty and fair practice in this area will earn the student easy marks in the exams.
• These are basic arithmetic problems and in most cases, a direct application of given formulas yields the answer.
• As these problems are relatively easier students should work hard on them as they prepare for the exam such that they answer these questions quickly and save time for the more difficult problems and sections.

## Most Recommended Books for Simple and Compound Interest

 Author Book Title N Tyra and K Kundan (Translator) Magical Book on Quicker Math (2018) R. S. Aggrawal Quantitative Aptitude for Competitive Exams (2017)

### Why prepare for Simple and Compound Interest from BYJU'S Exam Prep?

BYJU'S Exam Prep is an exam preparation platform that prepares students for various competitive exams in India including SSC and railway exams. It offers bilingual instruction -- in English and Hindi. The instruction includes the teaching of concepts, regular quizzes and the solving of old papers. Experts in various fields design the instruction manuals, student performance is thoroughly evaluated and students are given an all-India rank. The instruction and quizzes are designed keeping in mind the latest exam patterns. In addition, BYJU'S Exam Prep also provides full-fledged tests that can be procured for a price. This is an online portal, hence accessible from anywhere and it encourages healthy competition among students.

Ques: The difference between CI and SI on a certain amount at 10% interest rate for two years is Rs. 100. What is the principal amount?

Solution:

CI - SI = 100

SI = P x T x R / 100 = x x 2 x 10 / 100 = x /5

CI = P (1 + R/100)t − P = x (11/10)2 − x = 121/100x − x = 21/100x

CI - SI = 100

21/100x − x /5 =100

x = 10000

Ques: Calculate the simple interest on the amount of Rs. 10000 at the rate of 10.5% per annum from 6 March to 29 July 2020.

Solution

SI = P x N x R / 100

P = 10000

R = 105 / 10

T = [5 March - 29 June = 146 days or 2 / 5 of a year] 2 / 5

SI = 10000 x 105 x 2 / 100 x 10 x 5 = 420

Calculate the amount to be paid when simple interest is calculated on a principal amount of Rs. 2100, at a rate of 8.5% for 18 months.

Solution

SI = P x N x R / 100

P = 2100

N = 18 months [N refers to number of years. Hence 18 / 12] = 18 / 12 = 3 / 2

R = 8.5%

SI = 2100 x 85 x 3 / 100 x 2 x 10 = 267.75

A = P + SI = 2100 + 267.75 = Rs. 2367.75

Ques: The simple interest on a certain sum at the rate of 5% per year for 8 years is Rs. 2000. At what rate of interest can the same amount of interest be received on the same sum after 5 years.

Solution

SI = P x N x R / 100

2000 = P x 8 x 5 / 100

P = 5000

2000 = 5000 x 5 x N / 100

N = 8%

Ques: What will the compound interest at the rate of 12% on the principal amount of Rs. 50000 at the end of 4 years be?

Solution

A = P (1 + R/100)t

A = 50000 (1 + 12/100)4

A = 50000 (112/100)4

A = 50000 x 28/25 x 28/25 x 28/25 x 28/25

A = 78,675.968

CI = 78,675.968 - 50000 = 28,675.968

Ques: In how many years will an amount lent at 40% compound interest be more than doubled?

Solution

CI = A - P

A = P ( 1 + R/100 )t

As per the problem P ( 1 + R/100)t > 2P

( 1 + 40/100 )t > 2

(6/5)t > 2

6/5 x 6/5 / 6/5 > 2

t=3

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