Compound Interest Questions and Formulas for Aptitude Tests
Compound Interest Questions and Formulas for Aptitude Tests
Compound Interest is an important topic in quantitative aptitude. Questions based on compound interest are commonly connected with Simple Interest, percentages, profit and loss, discounts, and financial calculations.
At first, compound interest can look difficult because the interest is added back to the principal after every compounding period. But the underlying idea is simple:
In compound interest, interest earned during one period becomes part of the amount on which interest is calculated in the next period.
This is the main difference between compound interest and simple interest.
In this guide, you will learn the compound interest formula, understand how it works, solve common aptitude questions step by step, and practise the question types that frequently cause mistakes.
Quick answer
The basic compound amount formula is:
A = P(1 + R/100)^T
where:
- A = Amount
- P = Principal
- R = Rate of interest per year
- T = Time in years
Compound interest is:
CI = A − P
So:
CI = P(1 + R/100)^T − P
For example, if ₹10,000 is invested at 10% compound interest for 2 years:
A = 10,000(1 + 10/100)^2
A = 10,000 × 1.1²
A = ₹12,100
Therefore:
CI = ₹12,100 − ₹10,000 = ₹2,100
Try it with your own numbers:
What is compound interest?
Suppose you invest ₹10,000 at 10% interest per year.
During the first year, you earn:
10% of ₹10,000 = ₹1,000
Your amount becomes:
₹10,000 + ₹1,000 = ₹11,000
In the second year, interest is not calculated on ₹10,000.
It is calculated on ₹11,000.
Second-year interest:
10% of ₹11,000 = ₹1,100
So the amount becomes:
₹11,000 + ₹1,100 = ₹12,100
The extra ₹100 earned in the second year comes from earning interest on the previous year’s interest.
That is the basic idea behind compound interest.
Compound interest vs simple interest
The biggest difference between the two is the base on which interest is calculated.
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest calculated on | Original principal | Principal plus accumulated interest |
| Interest added to principal | No | Yes |
| Interest every year on same principal | Usually yes | No |
| Growth | Linear | Compounding growth |
| Basic formula | SI = PRT/100 | A = P(1 + R/100)^T |
For example, consider ₹10,000 at 10% per year for 2 years.
Simple Interest
SI:
10,000 × 10 × 2 / 100 = ₹2,000
Amount:
₹12,000
Compound Interest
Amount:
10,000 × (1.10)^2 = ₹12,100
Compound interest:
₹12,100 − ₹10,000 = ₹2,100
Therefore, for this example:
CI − SI = ₹100
₹10,000 at 10% per annum over 10 years — both lines start together, but CI pulls ahead as each year's interest starts earning its own interest.
Pocket Aptitude Tip: When a question says that interest is added to the principal or is compounded annually, think about compound interest rather than simple interest.
Practice this on the go
Get instant compound interest drills and more in the Pocket Aptitude app.
Compound interest formula
The standard formula for annual compounding is:
A = P(1 + R/100)^T
Then:
CI = A − P
Therefore:
CI = P[(1 + R/100)^T − 1]
Meaning of the variables
| Symbol | Meaning |
|---|---|
| P | Principal amount |
| R | Rate of interest per year |
| T | Time in years |
| A | Final amount |
| CI | Compound interest |
The formula works because the amount is multiplied by the same growth factor during each compounding period.
How the compound interest formula works
Suppose:
- P = ₹5,000
- R = 10%
- T = 2 years
After one year:
5,000 × 1.10 = ₹5,500
After two years:
5,500 × 1.10 = ₹6,050
Instead of calculating year by year, we can write:
A = 5,000 × 1.10²
A = ₹6,050
Therefore:
CI = ₹6,050 − ₹5,000
= ₹1,050
This is why the exponent T appears in the compound interest formula.
Remember: interest is always calculated on the previous total, not the original principal.
Example 1: Compound interest for 2 years
Find the compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually.
Example 2: Solve using year-by-year calculation
Find the compound interest on ₹10,000 at 10% per annum for 3 years.
Each year's total becomes next year's principal — that's the entire mechanism of compounding.
Year 1
Interest:
10% of ₹10,000 = ₹1,000
Amount:
₹11,000
Year 2
Interest:
10% of ₹11,000 = ₹1,100
Amount:
₹12,100
Year 3
Interest:
10% of ₹12,100 = ₹1,210
Amount:
₹13,310
Therefore:
CI = ₹13,310 − ₹10,000
= ₹3,310
Answer: ₹3,310
Which method should you use?
For a short question, year-by-year calculation can be easy to understand.
For longer periods, the formula is generally faster:
A = P(1 + R/100)^T
Example 3: Find the amount
₹15,000 is invested at 8% compound interest per annum for 2 years. Find the amount.
Using:
A = P(1 + R/100)^T
A = 15,000(1 + 8/100)²
A = 15,000 × 1.08²
A = 15,000 × 1.1664
A = ₹17,496
Answer: ₹17,496
Compound interest:
₹17,496 − ₹15,000 = ₹2,496
Example 4: Find the principal
The amount after 2 years at 10% compound interest is ₹12,100. Find the principal.
We know:
A = P(1 + R/100)^T
Substitute the values:
12,100 = P(1.10)²
12,100 = 1.21P
Therefore:
P = 12,100 / 1.21
P = ₹10,000
Answer: ₹10,000
Example 5: Find the rate of interest
An amount of ₹12,100 becomes ₹14,641 in 2 years when compounded annually. Find the rate.
Compound interest when the rate is 10%
A useful pattern appears when the rate is 10%.
Suppose the principal is ₹10,000.
| Year | Amount |
|---|---|
| Beginning | ₹10,000 |
| After 1 year | ₹11,000 |
| After 2 years | ₹12,100 |
| After 3 years | ₹13,310 |
| After 4 years | ₹14,641 |
The amount increases by 10% of the current amount each year.
This is the key idea behind compounding.
- At 10% p.a., the amount grows by 10% of the current amount each year, not the original principal.
- In Year 2, interest is earned on ₹11,000 — not ₹10,000.
- That's exactly why compound interest overtakes simple interest as time goes on.
Compound interest for half-yearly compounding
Sometimes the question says that interest is compounded half-yearly.
In that case:
- The number of compounding periods doubles.
- The rate for each period becomes half the annual rate.
So the formula becomes:
A = P(1 + R/200)^(2T)
Example
Find the amount on ₹10,000 at 10% per annum for 1 year, compounded half-yearly.
Half-yearly rate:
10% / 2 = 5%
Number of periods:
2
Therefore:
A = 10,000(1 + 5/100)²
A = 10,000 × 1.05²
A = ₹11,025
Therefore:
CI = ₹11,025 − ₹10,000
= ₹1,025
Compound interest for quarterly compounding
If interest is compounded quarterly:
- The annual rate is divided by 4.
- The number of periods is multiplied by 4.
The formula becomes:
A = P(1 + R/400)^(4T)
Example
₹20,000 is invested at 8% per annum for 1 year, compounded quarterly.
Quarterly rate:
8% / 4 = 2%
Number of quarters:
4
Therefore:
A = 20,000(1.02)^4
≈ ₹21,648.64
Therefore:
CI ≈ ₹1,648.64
Compound interest for different compounding periods
| Compounding | Rate per period | Number of periods |
|---|---|---|
| Annually | R | T |
| Half-yearly | R/2 | 2T |
| Quarterly | R/4 | 4T |
| Monthly | R/12 | 12T |
The important rule is:
When the compounding frequency changes, both the rate per period and the number of periods change.
This is one of the most common places where students make mistakes.
Try it yourself: change the principal, rate, or time below and switch between compounding frequencies to see how much the final amount shifts.
Compound interest for a fractional year
Some aptitude questions involve a time period such as 2½ years.
If interest is compounded annually and the question follows the usual school/aptitude convention of treating the full years by compounding and the remaining fraction separately, the exact method should be determined from the wording.
For example, if a question says that interest is compounded annually and gives a fractional period, check whether the question specifies how the fractional period should be handled.
Important: Do not automatically apply one method to every fractional-year question. Read the compounding condition carefully.
Difference between compound interest and simple interest
For a short period of 2 years, there is a useful formula for the difference between CI and SI when interest is compounded annually:
CI − SI = P(R/100)²
Example
Find the difference between compound interest and simple interest on ₹20,000 at 10% per annum for 2 years.
Using:
CI − SI = P(R/100)²
= 20,000 × (10/100)²
= 20,000 × 1/100
= ₹200
Therefore:
CI − SI = ₹200
Check
Simple interest:
20,000 × 10 × 2 / 100 = ₹4,000
Compound interest:
20,000(1.1)² − 20,000
= ₹24,200 − ₹20,000
= ₹4,200
Difference:
₹4,200 − ₹4,000 = ₹200
The formula gives the same result.
Important CI-SI difference formulas
For annual compounding:
For 2 years
CI − SI = P(R/100)²
For 3 years
CI − SI = P × [3(R/100)² + (R/100)³]
The 2-year formula is especially useful in aptitude tests because it can save calculation time.
When NOT to use the shortcut: Do not use the 2-year CI-SI difference formula for 3 years or for a different compounding frequency unless the appropriate formula applies.
Common mistakes in compound interest questions
1. Using the simple interest formula
A common mistake is:
SI = PRT/100
even when the question clearly says compound interest.
Remember that in compound interest, previous interest becomes part of the amount.
2. Forgetting to subtract the principal
The formula:
A = P(1 + R/100)^T
gives the amount, not the compound interest.
To find CI:
CI = A − P
3. Using the annual rate for half-yearly compounding
If the annual rate is 12% and interest is compounded half-yearly:
Rate per half-year = 6%, not 12%.
4. Forgetting to change the number of periods
For 3 years of half-yearly compounding:
Number of periods = 6, not 3.
5. Confusing amount and interest
If the final amount is ₹15,000 and the principal is ₹12,000:
Compound interest is:
₹15,000 − ₹12,000 = ₹3,000
The amount and interest are not the same thing.
6. Applying a shortcut outside its conditions
A formula that works for 2 years may not work for 3 years.
Always check the conditions before using a shortcut.
Fast approach for compound interest questions
For most aptitude questions, use this process:
- Identify the principal.
- Identify the annual rate.
- Identify the time.
- Check the compounding frequency.
- Convert the rate and number of periods if necessary.
- Calculate the amount.
- Subtract the principal if the question asks for compound interest.
- Check whether the answer is reasonable.
Pocket Aptitude speed tip
Before using the full formula, check whether the percentage has a simple form.
For example:
10% = 1/10
20% = 1/5
25% = 1/4
This can make calculations much faster.
Bonus: How fast does money double? (Rule of 72)
A quick way to estimate how many years it takes for a sum to double at a given compound interest rate is the Rule of 72:
Years to double ≈ 72 / R
Drag the slider to compare this estimate against the exact compound interest calculation:
Pocket Aptitude Tip: The Rule of 72 is a handy estimation shortcut for aptitude tests, but always confirm with the exact formula when the question demands precision.
Practice questions
Try solving these questions before checking the solutions.
Find the compound interest on ₹5,000 at 10% per annum for 2 years, compounded annually.
Show answer
₹1,050
Find the amount on ₹8,000 at 5% compound interest for 2 years.
Show answer
₹8,820
₹10,000 is invested at 20% compound interest per annum for 2 years. Find the compound interest.
Show answer
₹4,400
Find the difference between compound interest and simple interest on ₹20,000 at 10% per annum for 2 years.
Show answer
₹200
An amount of ₹14,400 becomes ₹17,424 in 2 years at compound interest. Find the annual rate.
Show answer
10%
Find the amount on ₹10,000 at 10% per annum for 2 years, compounded half-yearly.
Show answer
₹12,155.06 approximately
₹20,000 is invested at 8% per annum for 1 year, compounded quarterly. Find the compound interest.
Show answer
₹1,648.64 approximately
The amount on a certain principal at 10% compound interest for 2 years is ₹14,520. Find the principal.
Show answer
₹12,000
A sum of money is invested at 10% compound interest. If the principal is ₹20,000, find the amount after 3 years.
Show answer
₹26,620
What is the main difference between simple interest and compound interest?
Show answer
Simple interest is calculated on the original principal, while compound interest is calculated on the accumulated amount.
Frequently asked questions
What is the compound interest formula?
For annual compounding:
A = P(1 + R/100)^T
Then:
CI = A − P
What is the difference between compound interest and simple interest?
Simple interest is calculated on the original principal, while compound interest includes previously accumulated interest in the amount on which future interest is calculated.
How do I calculate compound interest for 2 years?
Use:
A = P(1 + R/100)²
Then subtract the principal:
CI = A − P
What happens when compound interest is calculated half-yearly?
The annual rate is divided by 2 and the number of compounding periods is multiplied by 2.
What happens when compound interest is calculated quarterly?
The annual rate is divided by 4 and the number of compounding periods is multiplied by 4.
What is the difference between amount and compound interest?
The amount is the final value including the principal and interest.
The compound interest is only the interest earned.
Therefore:
CI = Amount − Principal
Can I use the simple interest formula for compound interest?
No. The two formulas represent different methods of calculating interest.
What is the fastest way to solve compound interest questions?
First check the rate, time, and compounding frequency. Then look for simple percentage conversions or a suitable shortcut before using the full formula.
Is the compound interest formula important for aptitude exams?
Yes. You should understand the standard formula and also know how to handle annual, half-yearly, and quarterly compounding.
Related Pocket Aptitude topics
Compound Interest is closely connected to these other arithmetic topics:
Quick self-check
Before you go, try these three — pick an answer and the full solution appears immediately.
Find the compound interest on ₹12,000 at 10% per annum for 2 years, compounded annually.
🤔 Without calculating, what do you think?
👇 Pick an option to see the answer
Find the difference between compound interest and simple interest on ₹15,000 at 10% per annum for 2 years.
🤔 Without calculating, what do you think?
👇 Pick an option to see the answer
₹8,000 is invested at 8% per annum for 1 year, compounded half-yearly. Find the amount.
🤔 Without calculating, what do you think?
👇 Pick an option to see the answer
Summary
Compound interest becomes much easier once you understand one central idea:
Interest earned in one period becomes part of the amount used to calculate interest in the next period.
The most important formulas are:
A = P(1 + R/100)^T
and:
CI = A − P
For different compounding frequencies, remember to adjust both the rate and the number of periods.
For aptitude tests, focus on:
- Understanding the difference between SI and CI
- Applying the basic compound interest formula
- Calculating amount and compound interest correctly
- Handling half-yearly and quarterly compounding
- Recognising when a shortcut can be used
- Avoiding mistakes with the rate and number of periods
Once the basic formula is comfortable, practise mixed questions under a time limit. Accuracy should come first; speed will improve with repeated practice.