Simple Interest and Compound Interest are important topics in mathematics and quantitative aptitude. These concepts are used in banking, loans, savings, fixed deposits, business, investments, and competitive exams. If you understand principal, rate, time, interest, and amount, most questions from this chapter become easy.
Interest is the extra money paid for using someone else’s money or earned by investing money. The original money is called principal. The percentage charged or earned is called rate of interest. The duration for which money is borrowed or invested is called time.
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus previously earned interest. This is the main difference between the two.
This lesson explains simple interest and compound interest in simple language with formulas, examples, difference table, compounding cases, present worth, practice questions, and FAQs. The existing formula images in this post are kept as they are.
Important Terms
| Term | Meaning |
|---|---|
| Principal | Original money borrowed or invested |
| Interest | Extra money paid or earned |
| Rate | Interest percentage per time period |
| Time | Duration of loan or investment |
| Amount | Principal plus interest |
Existing Formulas
Simple interest
P= principal amount
R = rate/unit
T = time/year month day etc.
Compound interest
P= principal amount
R= rate/unit
T= time unit
Where rate are difference for different unit or time.
Than 
Present worth of Rs x lac in year hence is given by present worth=
What Is Simple Interest?
Simple Interest, or SI, is interest calculated only on the principal amount. The interest does not get added to the principal for the next period.
Formula:
SI = P × R × T / 100
Here P is principal, R is rate percent per annum, and T is time in years.
Amount under simple interest:
Amount = Principal + Simple Interest.
Example: Find simple interest on Rs. 10000 at 5 percent per annum for 3 years.
SI = 10000 × 5 × 3 / 100 = Rs. 1500.
Amount = 10000 + 1500 = Rs. 11500.
What Is Compound Interest?
Compound Interest, or CI, is interest calculated on principal as well as on previous interest. It is often called interest on interest.
Formula for amount when interest is compounded annually:
A = P(1 + R/100)n
Compound Interest = Amount – Principal.
Example: Find compound interest on Rs. 10000 at 10 percent per annum for 2 years.
A = 10000(1 + 10/100)2.
A = 10000(1.1)2 = 10000 × 1.21 = Rs. 12100.
CI = 12100 – 10000 = Rs. 2100.
Difference Between Simple Interest and Compound Interest
| Point | Simple Interest | Compound Interest |
|---|---|---|
| Calculated on | Only principal | Principal plus previous interest |
| Growth | Linear | Faster over time |
| Formula | SI = PRT/100 | A = P(1 + R/100)n |
| Best for | Simple loans and short-term calculation | Investments and long-term growth |
| Interest each year | Same every year | Changes every year |
Simple Interest Formula Variations
If SI, R, and T are known, principal can be found as:
P = SI × 100 / (R × T)
If SI, P, and T are known, rate can be found as:
R = SI × 100 / (P × T)
If SI, P, and R are known, time can be found as:
T = SI × 100 / (P × R)
Simple Interest Examples
Example 1
Find SI on Rs. 8000 at 6 percent per annum for 5 years.
SI = 8000 × 6 × 5 / 100 = Rs. 2400.
Amount = 8000 + 2400 = Rs. 10400.
Example 2
A sum becomes Rs. 5600 in 4 years at 10 percent simple interest. Find the principal.
Let principal be P.
SI for 4 years = 40 percent of P.
Amount = P + 40 percent of P = 140 percent of P.
So 140 percent of P = 5600.
P = 5600 × 100 / 140 = Rs. 4000.
Example 3
Simple interest on Rs. 12000 for 3 years is Rs. 1800. Find rate.
R = SI × 100 / (P × T).
R = 1800 × 100 / (12000 × 3) = 5 percent.
Compound Interest Formula for Different Compounding Periods
If interest is compounded more than once in a year, rate and time must be adjusted.
| Compounding type | Rate used | Number of periods |
|---|---|---|
| Annually | R | T |
| Half-yearly | R/2 | 2T |
| Quarterly | R/4 | 4T |
| Monthly | R/12 | 12T |
Example: Rs. 10000 is invested at 12 percent per annum compounded half-yearly for 1 year.
Rate per half-year = 12/2 = 6 percent.
Number of half-years = 2.
A = 10000(1 + 6/100)2.
A = 10000 × 1.1236 = Rs. 11236.
CI = Rs. 1236.
Compound Interest with Different Rates
If rates are different for different years, multiply year-wise factors.
A = P(1 + R1/100)(1 + R2/100)(1 + R3/100) …
Example: Find amount on Rs. 10000 if rates are 5 percent, 10 percent, and 20 percent for three successive years.
A = 10000(1.05)(1.10)(1.20).
A = 10000 × 1.386 = Rs. 13860.
CI = 13860 – 10000 = Rs. 3860.
Present Worth
Present worth means the value today of an amount due in the future. It is used when money grows with compound interest.
Present Worth = Future Amount / (1 + R/100)n
Example: What is the present worth of Rs. 12100 due after 2 years at 10 percent compound interest?
Present worth = 12100 / (1.1)2 = 12100 / 1.21 = Rs. 10000.
Difference Between SI and CI for 2 Years
For 2 years, the difference between compound interest and simple interest is:
Difference = P(R/100)2
Example: Find the difference between CI and SI on Rs. 10000 at 10 percent for 2 years.
Difference = 10000 × (10/100)2.
= 10000 × 1/100 = Rs. 100.
Simple interest = Rs. 2000.
Compound interest = Rs. 2100.
Difference = Rs. 100.
Interest for Months and Days
In simple interest, time must be converted into years if the rate is annual.
6 months = 1/2 year.
3 months = 1/4 year.
9 months = 3/4 year.
Example: Find SI on Rs. 6000 at 8 percent per annum for 6 months.
T = 1/2.
SI = 6000 × 8 × 1/2 / 100 = Rs. 240.
Amount at Simple Interest from Two Amounts
If amount at two different times is given, the difference gives interest for the difference in time.
Example: A sum amounts to Rs. 815 in 3 years and Rs. 854 in 4 years at simple interest. Find the principal.
Interest for 1 year = 854 – 815 = Rs. 39.
Interest for 3 years = 39 × 3 = Rs. 117.
Principal = 815 – 117 = Rs. 698.
Worked Examples
Example 1
Find SI on Rs. 15000 at 12 percent for 2 years.
SI = 15000 × 12 × 2 / 100 = Rs. 3600.
Example 2
Find amount on Rs. 5000 at 8 percent simple interest for 4 years.
SI = 5000 × 8 × 4 / 100 = Rs. 1600.
Amount = 5000 + 1600 = Rs. 6600.
Example 3
Find CI on Rs. 20000 at 10 percent for 2 years compounded annually.
A = 20000(1.1)2 = 24200.
CI = 24200 – 20000 = Rs. 4200.
Example 4
A sum increases by 60 percent in 6 years at simple interest. Find the annual rate.
If P = 100, SI = 60, T = 6.
R = 60 × 100 / (100 × 6) = 10 percent.
Example 5
At 10 percent compound interest, find CI on Rs. 12000 for 3 years.
A = 12000(1.1)3 = 12000 × 1.331 = Rs. 15972.
CI = 15972 – 12000 = Rs. 3972.
Real Life Uses
Simple interest is often used in short-term borrowing and basic loan calculations. It is easy to calculate because interest remains the same every year.
Compound interest is important for long-term investments because interest earns more interest. Savings, fixed deposits, mutual funds, and debt calculations often use compound growth ideas.
For borrowers, compound interest can become costly if unpaid interest keeps getting added to the balance. For investors, compound interest can help money grow faster over time.
Common Mistakes
- Using compound interest formula for simple interest questions.
- Forgetting to subtract principal from amount to get CI.
- Not converting months into years.
- Using annual rate directly for half-yearly or quarterly compounding.
- Confusing amount with interest.
- Not checking whether rate is annual, monthly, or for some other period.
Practice Questions
- Find SI on Rs. 10000 at 7 percent for 3 years.
- Find amount on Rs. 8000 at 5 percent SI for 4 years.
- Find principal if SI is Rs. 2400, rate is 8 percent, and time is 5 years.
- Find rate if SI on Rs. 12000 for 2 years is Rs. 1920.
- Find CI on Rs. 5000 at 10 percent for 2 years.
- Find amount on Rs. 16000 at 5 percent compounded annually for 2 years.
- Find CI on Rs. 10000 at 12 percent compounded half-yearly for 1 year.
- Find the difference between CI and SI on Rs. 20000 at 10 percent for 2 years.
Answers to Practice Questions
- Rs. 2100.
- Rs. 9600.
- Rs. 6000.
- 8 percent.
- Rs. 1050.
- Rs. 17640.
- Rs. 1236.
- Rs. 200.
Frequently Asked Questions
What is simple interest?
Simple interest is interest calculated only on the principal amount.
What is compound interest?
Compound interest is interest calculated on principal plus previously earned interest.
What is the formula of SI?
SI = P × R × T / 100.
What is amount?
Amount is principal plus interest.
Why is compound interest more than simple interest?
Compound interest is usually more because interest is added to the principal and earns further interest.
What changes in half-yearly compounding?
The annual rate is divided by 2 and the number of periods is multiplied by 2.
What is present worth?
Present worth is the current value of a future amount after discounting compound interest.
How to Decide Which Formula to Use
Many students make mistakes in this chapter because they start calculation before reading the question fully. First decide whether the question is based on simple interest or compound interest. Then check whether the question asks for interest, amount, principal, rate, or time.
If the question says that interest is calculated on the original sum only, use simple interest. If the question says interest is compounded annually, half-yearly, quarterly, or monthly, use compound interest. If the question gives amount after two different years under simple interest, subtract the amounts to find interest for the extra time.
A good habit is to write the given values separately. Write P for principal, R for rate, T for time, SI for simple interest, CI for compound interest, and A for amount. After that, substitute values in the formula. This keeps the solution clean and reduces confusion.
Simple Interest Shortcut Ideas
Simple interest grows by the same amount every year. Because of this, percentage thinking is very useful. At 10 percent per year, simple interest for 3 years is 30 percent of principal. At 8 percent per year for 5 years, simple interest is 40 percent of principal.
Example: A sum becomes Rs. 15000 in 5 years at 10 percent simple interest. Find the principal.
In 5 years, simple interest = 50 percent of principal.
Amount = 150 percent of principal.
So 150 percent of P = 15000.
P = 15000 × 100 / 150 = Rs. 10000.
This method is faster than writing the full formula every time. It is especially helpful in aptitude exams where options are given.
Finding Rate from Amount
Sometimes the question gives principal, amount, and time. In such cases, first find interest by subtracting principal from amount. Then use the rate formula.
Example: A man invests Rs. 9000 and receives Rs. 10800 after 4 years at simple interest. Find the rate.
Interest = 10800 – 9000 = Rs. 1800.
R = SI × 100 / (P × T).
R = 1800 × 100 / (9000 × 4) = 5 percent.
Always remember that rate is normally per annum unless another period is clearly mentioned.
Finding Time from Amount
When principal, amount, and rate are given, first calculate interest and then find time.
Example: In how many years will Rs. 7500 become Rs. 9300 at 8 percent simple interest?
SI = 9300 – 7500 = Rs. 1800.
T = SI × 100 / (P × R).
T = 1800 × 100 / (7500 × 8) = 3 years.
If the answer comes in decimal form, convert it into months if needed. For example, 1.5 years means 1 year 6 months.
Compound Interest Step-by-Step Method
Compound interest questions become easier when you calculate amount period by period. This method is useful when the time is small, such as 2 or 3 years.
Example: Find the compound interest on Rs. 8000 at 5 percent per annum for 3 years.
First year amount = 8000 + 5 percent of 8000 = 8400.
Second year amount = 8400 + 5 percent of 8400 = 8820.
Third year amount = 8820 + 5 percent of 8820 = 9261.
Compound interest = 9261 – 8000 = Rs. 1261.
This method also shows why compound interest is more than simple interest. In the second and third year, interest is calculated on a larger balance.
Compound Interest for Fractional Time
Some questions contain time like 2 years 6 months. For compound interest, handle the complete years first and then handle the remaining fractional part. The fractional part may be treated as simple interest on the amount after complete years unless the question gives a special compounding condition.
Example: Find amount on Rs. 10000 at 10 percent compound interest for 2 years 6 months.
Amount for first 2 years = 10000(1.1)2 = Rs. 12100.
Interest for remaining 6 months at 10 percent = 12100 × 10 × 1/2 / 100 = Rs. 605.
Total amount = 12100 + 605 = Rs. 12705.
Therefore CI = 12705 – 10000 = Rs. 2705.
Quarterly and Monthly Compounding
In quarterly compounding, the year is divided into four parts. The rate for each quarter is R/4 and the number of periods is 4T. In monthly compounding, the rate for each month is R/12 and the number of periods is 12T.
Example: Find amount on Rs. 12000 at 8 percent per annum compounded quarterly for 1 year.
Quarterly rate = 8/4 = 2 percent.
Number of quarters = 4.
A = 12000(1.02)4.
A = 12000 × 1.08243216 = Rs. 12989.19 approximately.
CI = Rs. 989.19 approximately.
For school and aptitude exams, answers may be rounded to the nearest rupee unless the question asks for exact decimal value.
Comparing Two Schemes
Interest questions often ask which scheme is better. One scheme may offer simple interest and another may offer compound interest. Compare the final amounts, not just the rate.
Example: Which is better for Rs. 10000 for 2 years: 10 percent simple interest or 10 percent compound interest annually?
Under simple interest, SI = 10000 × 10 × 2 / 100 = Rs. 2000. Amount = Rs. 12000.
Under compound interest, amount = 10000(1.1)2 = Rs. 12100. CI = Rs. 2100.
Compound interest gives Rs. 100 more in this case.
If time is only one year and the rate is same, simple interest and compound interest are equal. The difference starts from the second year onward.
When CI and SI Difference Is Given
For 2 years, the difference between CI and SI is very useful. It comes from interest earned on the first year’s interest.
Difference = P × R × R / 10000.
Example: The difference between compound interest and simple interest on a sum for 2 years at 5 percent is Rs. 25. Find the sum.
25 = P × 5 × 5 / 10000.
25 = P × 25 / 10000.
P = 25 × 10000 / 25 = Rs. 10000.
This shortcut is common in competitive exams. It saves time because you do not need to calculate SI and CI separately.
Depreciation and Compound Interest
Compound interest formula is not only used for growth. It is also used for depreciation, where the value of an item decreases every year by a fixed percentage.
If an item loses value at R percent per year, then:
Value after n years = P(1 – R/100)n.
Example: A machine worth Rs. 50000 depreciates by 10 percent every year. Find its value after 2 years.
Value = 50000(1 – 10/100)2.
Value = 50000(0.9)2 = 50000 × 0.81 = Rs. 40500.
Loss in value = 50000 – 40500 = Rs. 9500.
Present Worth in Loan and Discount Questions
Present worth questions ask what amount should be paid today to equal a future amount. These questions use the reverse of compound interest. Instead of growing principal into future amount, we discount future amount back to present value.
Example: What sum invested today at 20 percent compound interest will become Rs. 1728 after 3 years?
P = A / (1 + R/100)n.
P = 1728 / (1.2)3.
P = 1728 / 1.728 = Rs. 1000.
So Rs. 1000 is the present worth of Rs. 1728 due after 3 years at 20 percent compound interest.
Mixed Practice Examples
Example 6
A sum earns Rs. 450 as simple interest in 3 years at 5 percent per annum. Find the principal.
P = 450 × 100 / (5 × 3) = Rs. 3000.
Example 7
A sum becomes double itself in 8 years at simple interest. Find the rate.
If principal is 100, amount is 200, so interest is 100.
R = 100 × 100 / (100 × 8) = 12.5 percent.
Example 8
A sum becomes Rs. 13310 in 3 years at 10 percent compound interest. Find the principal.
P = 13310 / (1.1)3 = 13310 / 1.331 = Rs. 10000.
Example 9
Find the compound interest on Rs. 64000 for 1 year at 10 percent per annum compounded half-yearly.
Half-yearly rate = 5 percent, number of periods = 2.
A = 64000(1.05)2 = 64000 × 1.1025 = Rs. 70560.
CI = Rs. 6560.
Example 10
A sum amounts to Rs. 7200 in 2 years and Rs. 7800 in 3 years at simple interest. Find the principal.
Interest for 1 year = 7800 – 7200 = Rs. 600.
Interest for 2 years = Rs. 1200.
Principal = 7200 – 1200 = Rs. 6000.
Extra Practice Questions
- A sum of Rs. 5000 is lent at 9 percent simple interest for 4 years. Find SI and amount.
- At what rate will Rs. 12000 give Rs. 3600 simple interest in 5 years?
- In how many years will Rs. 16000 become Rs. 20800 at 6 percent simple interest?
- Find CI on Rs. 25000 at 8 percent for 2 years compounded annually.
- Find amount on Rs. 18000 at 12 percent for 1 year compounded half-yearly.
- The difference between CI and SI for 2 years at 10 percent is Rs. 75. Find the principal.
- A machine worth Rs. 90000 depreciates by 20 percent per year. Find its value after 2 years.
- Find present worth of Rs. 14641 due after 2 years at 10 percent compound interest.
Answers to Extra Practice Questions
- SI = Rs. 1800, amount = Rs. 6800.
- 6 percent.
- 5 years.
- Rs. 4160.
- Rs. 20224.80.
- Rs. 7500.
- Rs. 57600.
- Rs. 12100.
Revision Notes
Simple interest is best understood as fixed yearly interest. Compound interest is best understood as growing balance. In simple interest, the interest for every year is the same. In compound interest, the interest for every year changes because the amount changes.
For quick revision, remember these four steps: identify the type of interest, write the given values, adjust rate and time if compounding is not annual, and check whether the final answer should be interest or amount.
In exams, also check the wording carefully. If the question says “amounts to,” it is giving final amount. If it says “interest earned,” it is giving only interest. If it says “compounded half-yearly,” divide the rate by 2 and multiply the time by 2.
Conclusion
Simple interest is based only on principal, while compound interest is based on principal plus accumulated interest. This difference makes compound interest grow faster over time.
To solve questions correctly, identify principal, rate, time, and whether the question asks for interest or amount. Then choose the correct formula and handle time conversion carefully.