In the previous chapter, we learned the basic concepts of Simple Interest (SI) and Compound Interest (CI), understood the difference between them, and explored their applications in competitive exams.
In this chapter, we’ll study the Simple Interest and Compound Interest formulas in detail. You’ll learn what each formula means, how it is derived, when to use it, and how to apply it to different types of questions commonly asked in SSC, RRB, Banking, Defence, Police, and other competitive examinations.
By the end of this chapter, you’ll have a clear understanding of the Simple Interest (SI) and Compound Interest (CI) formulas and the confidence to apply them to a variety of exam-level problems.
Before we begin, you can also explore our Quantitative Aptitude Notes, Quantitative Aptitude Formulas, Quantitative Aptitude Practice Questions, Quantitative Aptitude Previous Year Questions (PYQs), Math Calculators, and Quantitative Aptitude Syllabus sections for additional learning, revision, and exam preparation.
Let’s start by understanding the variables used in the Simple Interest and Compound Interest formulas.
Simple Interest & Compound Interest Formula Sheet
| Formula | Expression |
| Simple Interest | SI = (P × R × T) ÷ 100 |
| Principal (SI) | P = (SI × 100) ÷ (R × T) |
| Rate (SI) | R = (SI × 100) ÷ (P × T) |
| Time (SI) | T = (SI × 100) ÷ (P × R) |
| Amount (SI) | A = P(1 + RT/100) |
| Amount (CI) | A = P(1 + R/100)ⁿ |
| Compound Interest | CI = A − P |
| Compound Interest | CI = P[(1 + R/100)ⁿ − 1] |
| Principal (CI) | P = A ÷ (1 + R/100)ⁿ |
| Principal (using CI) | P = CI ÷ [(1 + R/100)ⁿ − 1] |
| Rate (CI) | R = [(A/P)^(1/n) − 1] × 100 |
Simple Interest Formula & Applications
Before learning the formula, let’s first understand why it is called Simple Interest.
In Simple Interest, the interest is always calculated on the same principal amount. It never changes throughout the entire period.
Suppose you borrow ₹10,000.
Whether the loan is for 1 year, 2 years, or 5 years, the interest is always calculated on ₹10,000. The interest earned in previous years is not added to the principal for future calculations.
| Year | Principal Amount | Interest Earned (10% p.a.) |
| 1 | ₹10,000 | ₹1,000 |
| 2 | ₹10,000 | ₹1,000 |
| 3 | ₹10,000 | ₹1,000 |
| 4 | ₹10,000 | ₹1,000 |
| 5 | ₹10,000 | ₹1,000 |
Notice that both the principal amount and the interest earned remain the same every year.
That is why it is called Simple Interest.
Now let’s see the formula used to calculate it.
Formula
SI = (P × R × T) ÷ 100
where
- P = Principal Amount
- R = Rate of Interest
- T = Time
- SI = Simple Interest
Important: The rate of interest and the time period must always be expressed in the same unit.
- If the rate is per annum, the time should be in years.
- If the rate is per month, the time should be in months.
- If the rate is per quarter, the time should be in quarters.
Example 1: Rate Given Per Annum
A shopkeeper takes a loan of ₹10,000 at 10% simple interest per annum and has to repay it after 6 months.
Given:
- P = ₹10,000
- R = 10% per annum
- T = 6 months = ½ year
Using the formula,
SI = (P × R × T) ÷ 100
SI = (10,000 × 10 × ½) ÷ 100
SI = ₹500
Therefore, the Simple Interest = ₹500.
Example 2: Rate Given Per Month
Now, suppose the rate of interest is 10% per month instead of 10% per annum, while the principal and loan period remain the same.
Given:
- P = ₹10,000
- R = 10% per month
- T = 6 months
Using the formula,
SI = (10,000 × 10 × 6) ÷ 100
SI = ₹6,000
Therefore, the Simple Interest = ₹6,000.
Why are the answers different?
Although the principal amount and the loan period are the same in both examples, the unit of the interest rate is different.
- In Example 1, the rate is 10% per annum, which means 10% for one year. Therefore, the loan period of 6 months must be converted to ½ year.
- In Example 2, the rate is 10% per month, which means 10% for one month. Since the loan period is already given in months, no conversion is required.
Note: The time period and the rate of interest must be expressed in the same unit before applying the Simple Interest formula.
Rearranging the Simple Interest Formula
If any three values are known, the fourth value can be calculated.
Principal Formula
If SI, R, and T are known,
P = (SI × 100) ÷ (R × T)
Example 3: A bank employee earned ₹1,500 as simple interest at 5% per annum in 3 years on a fixed deposit. Find the principal amount.
Given:
SI = ₹1,500
R = 5% per annum
T = 3 years
Solution:
P = (SI × 100) ÷ (R × T)
P = (1500 × 100) ÷ (5 × 3)
P = 150000 ÷ 15
P = ₹10,000
Principal Amount = ₹10,000.
Rate of Interest Formula
If SI, P, and T are known,
R = (SI × 100) ÷ (P × T)
Example 4: A Station Master invested ₹20,000 and earned ₹3,000 as simple interest in 3 years. Find the rate of interest per annum.
Given:
SI = ₹3,000
P = ₹20,000
T = 3 years
Solution:
R = (SI × 100) ÷ (P × T)
R = (3000 × 100) ÷ (20000 × 3)
R = 300000 ÷ 60000
R = 5% per annum
Rate of Interest = 5% per annum.
Time Formula
If SI, P, and R are known,
T = (SI × 100) ÷ (P × R)
Example 5: An Assistant Section Officer (ASO) invested ₹8,000 at 10% per annum and earned ₹1,600 as simple interest. Find the time.
Given:
SI = ₹1,600
P = ₹8,000
R = 10% per annum
Solution:
T = (SI × 100) ÷ (P × R)
T = (1600 × 100) ÷ (8000 × 10)
T = 160000 ÷ 80000
T = 2 years
Time = 2 years.
Amount Formula in Simple Interest
The total amount at the end of the specified time period is the sum of the principal and the simple interest.
Amount = Principal + Simple Interest
Substituting the Simple Interest formula,
Amount = P + (P × R × T) ÷ 100
Taking P common,
Amount = P × (1 + RT/100)
or simply,
A = P × (1 + RT/100)
where,
- A = Amount
- P = Principal
- R = Rate of Interest
- T = Time
Example 6: A Section Officer invested ₹10,000 at 8% per annum for 2 years. Find the total amount at the end of the investment period.
Given:
P = ₹10,000
R = 8% per annum
T = 2 years
Solution:
Simple Interest = (P × R × T) ÷ 100
SI = (10000 × 8 × 2) ÷ 100
SI = ₹1,600
Amount = Principal + Simple Interest
A = 10,000 + 1,600
A = ₹11,600
Total Amount = ₹11,600.
Note: Using the Simple Interest formula, you can calculate:
- Simple Interest (SI)
- Principal Amount (P)
- Rate of Interest (R)
- Time (T)
- Total Amount (A)
In Simple Interest, the interest is always calculated on the same principal amount.
But what happens if the interest earned every year is added to the principal, and the next year’s interest is calculated on this new amount?
This is called Compound Interest. Let’s understand it in the next section.
Compound Interest Formula & Applications
In the previous chapter, we learned that
Compound Interest = Amount − Principal
where,
- Amount (A) = Principal + Compound Interest
- Principal (P) = Original amount borrowed or invested
Now let’s understand how the Compound Interest formula is derived.
The key idea behind Compound Interest is that the interest earned in one year is added to the principal. As a result, the next year’s interest is calculated on this increased principal.
Suppose you borrow ₹10,000 from your friend at 10% compound interest per annum and agree to repay it after 4 years.
After the 1st Year
Interest = 10,000 × 10 ÷ 100 = ₹1,000
Amount after 1st year
= 10,000 + 1,000
= ₹11,000
Now write it in terms of P.
Amount after 1st year
= P + (P × R)/100
Taking P common,
Amount after 1st year = P(1 + R/100)
After the 2nd Year
Now the principal is no longer ₹10,000.
It becomes ₹11,000.
Interest
= 11,000 × 10 ÷100
= ₹1,100
Amount
= 11,000 + 1,100
Now substitute the previous year’s amount.
Amount
= P(1 + R/100) + P(1 + R/100) × R/100
Take P(1 + R/100) common.
Amount after 2nd year
= P(1 + R/100)²
After the 3rd Year
Similarly,
Amount after 3rd year
= P(1 + R/100)³
After the 4th Year
Amount after 4th year
= P(1 + R/100)⁴
Notice the pattern. Every year, the amount is multiplied by (1 + R/100) once. Therefore, after n years, this factor is multiplied n times, giving the formula: A = P(1 + R/100)ⁿ
For our example,
= 10000(1 + 10/100)⁴
= 10000 × 1.1⁴
A= ₹14,641
Therefore,
Compound Interest = Amount − Principal
= 14,641 − 10,000
= ₹4,641
Notice how the principal changes every year because the interest earned is added to it.
Principal at the beginning of Year 1 = ₹10,000
Principal at the beginning of Year 2 = ₹11,000
Compound Interest Formula
If the money is invested for n years, then
Amount = P(1 + R/100)ⁿ
Therefore,
Compound Interest = P(1 + R/100)ⁿ − P
where, A = Amount P = Principal Amount R = Rate of Interest n = Number of years (or compounding periods)
Example 7: An Ola driver deposits ₹20,000 in a savings scheme that offers 10% compound interest per annum. Find the Compound Interest earned after 2 years.
Given:
P = ₹20,000
R = 10% per annum
n = 2 years
Solution:
Amount = P(1 + R/100)ⁿ
A = 20,000(1 + 10/100)²
A = 20,000 × (1.1)²
A = 20,000 × 1.21
A = ₹24,200
Compound Interest = A − P
= 24,200 − 20,000
= ₹4,200
Compound Interest = ₹4,200.
Example 8: Ramada Hotel, Jaipur invests ₹50,000 in a fixed deposit at 8% compound interest per annum for 2 years. Find the total amount at maturity.
Given:
P = ₹50,000
R = 8% per annum
n = 2 years
Solution:
Amount = P(1 + R/100)ⁿ
A = 50,000(1 + 8/100)²
A = 50,000 × (1.08)²
A = 50,000 × 1.1664
A = ₹58,320
The Amount = ₹58,320.
Example 9: Raskhan invested an amount at 10% compound interest per annum. After 2 years, the investment grew to ₹24,200. Find the original principal amount.
Given:
A = ₹24,200
R = 10% per annum
n = 2 years
Solution:
A = P(1 + R/100)ⁿ
24,200 = P(1.10)²
24,200 = P × 1.21
P = 24,200 ÷ 1.21
P = ₹20,000
Principal Amount = ₹20,000.
Example 10: An Uber driver invested ₹20,000 in a savings scheme. After 2 years, the amount became ₹24,200 under compound interest. Find the annual rate of interest.
Given:
P = ₹20,000
A = ₹24,200
n = 2 years
Solution:
A = P(1 + R/100)²
24,200 = 20,000(1 + R/100)²
1.21 = (1 + R/100)²
√1.21 = 1 + R/100
1.10 = 1 + R/100
R/100 = 0.10
R = 10%
Rate of Interest = 10% per annum.
Practice Questions
Question 1: A truck driver invested ₹40,000 in a fixed deposit at 9% compound interest per annum for 2 years. Find:
(a) Amount
(b) Compound Interest
Question 2: A Section Controller in the Indian Railways invested ₹60,000 at 7% simple interest per annum for 4 years. Find:
(a) Simple Interest
(b) Total Amount
Now that you’ve learned the formulas and solved the examples, strengthen your concepts by practicing more questions.
Practice Simple Interest & Compound Interest Questions with Answer Keys
This practice set includes beginner to exam-level questions commonly asked in SSC, RRB, Banking, Defence, Police, and other competitive examinations.
What We Learned
In this chapter, we learned:
- The Simple Interest (SI) formula and its applications.
- The Compound Interest (CI) formula and how it is derived.
- How to calculate the Amount using both Simple Interest and Compound Interest.
- How to find the Principal, Rate of Interest, and Time using the Simple Interest formula.
- Why the principal remains constant in Simple Interest but changes every year in Compound Interest.
- How to solve Simple Interest and Compound Interest questions commonly asked in SSC, RRB, Banking, Defence, Police, and other competitive examinations.
FAQ
1. What is the formula for calculating Simple Interest?
The formula for calculating Simple Interest (SI) is:
SI = (P × R × T) ÷ 100
where:
P = Principal Amount
R = Rate of Interest
T = Time Period
SI = Simple Interest
2. What is the formula for calculating Compound Interest?
The formula for calculating Compound Interest (CI) is:
CI = A − P
where:
A = Amount
P = Principal Amount
The amount is calculated using the formula:
A = P(1 + R/100)ⁿ
where R is the annual rate of interest and n is the number of years (or compounding periods).
3. Why should the rate of interest and time be in the same unit?
The rate of interest and the time period must be expressed in the same unit to calculate the correct interest. For example, if the rate is per annum, the time should be in years. If the rate is per month, the time should be in months.
4. Which competitive exams ask Simple Interest and Compound Interest questions?
Simple Interest and Compound Interest questions are commonly asked in SSC CGL, SSC CHSL, SSC MTS, RRB NTPC, RRB Group D, Banking, Defence, NDA, CDS, State Police, and other competitive examinations. If you’re preparing for any of these exams and want to check the latest notifications, eligibility, syllabus, exam pattern, and recruitment updates, you can also visit our JobshubIndia.com portal.
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