Simple Interest vs Compound Interest: Key Differences, Formulas and Examples
Simple interest and compound interest are two methods used to calculate interest on money borrowed or invested. The main difference is that simple interest is calculated only on the original principal, while compound interest is calculated on the principal plus previously accumulated interest.
Understanding simple interest vs compound interest is important when comparing loans, deposits, investments and other financial products. Over longer periods, compounding can create a significant difference in the final amount. The Reserve Bank of India explains compounding as earning interest on the principal as well as previously earned interest.
Quick Information
| Particular | Simple Interest | Compound Interest |
| Interest calculated on | Original principal | Principal + accumulated interest |
| Interest on interest | No | Yes |
| Growth pattern | Relatively linear | Can accelerate over time |
| Formula | SI = P × R × T / 100 | A = P(1 + r/n)^(nt) |
| Long-term growth | Generally lower | Generally higher at the same rate |
| Common relevance | Certain financial calculations | Investments, deposits and various debt calculations |
| Effect of time | Moderate | Becomes more significant over longer periods |
What Is Simple Interest?
Simple interest is interest calculated only on the original principal amount throughout the specified period.
For example, suppose you invest ₹10,000 at 10% simple interest for three years.
The interest for each year remains:
₹10,000 × 10% = ₹1,000
Over three years:
Total Interest = ₹1,000 × 3 = ₹3,000
Therefore:
Final Amount = ₹10,000 + ₹3,000 = ₹13,000
The interest does not get added to the principal for calculating the next year’s interest.
Simple Interest Formula
The standard formula is:
SI = P × R × T / 100
Where:
- SI = Simple Interest
- P = Principal amount
- R = Annual interest rate
- T = Time period in years
The final amount can be calculated as:
A = P + SI
Simple Interest Example
Suppose:
- Principal = ₹50,000
- Interest rate = 8% per year
- Time = 2 years
Then:
SI = ₹50,000 × 8 × 2 / 100
SI = ₹8,000
Therefore:
Final Amount = ₹50,000 + ₹8,000 = ₹58,000
What Is Compound Interest?
Compound interest means that the interest earned is added to the principal, and future interest is calculated on the increased amount.
This is commonly described as interest on interest. RBI’s financial education material illustrates how ₹10,000 earning 10% compounded annually becomes ₹11,000 after the first year, ₹12,100 after the second year and ₹13,310 after the third year.
For example:
- Initial amount = ₹10,000
- First-year interest = ₹1,000
- New balance = ₹11,000
- Second-year interest = ₹1,100
- New balance = ₹12,100
The second year’s interest is higher because it is calculated on ₹11,000 rather than ₹10,000.
Compound Interest Formula
The general compound amount formula is:
A = P(1 + r/n)^(nt)
Where:
- A = Final amount
- P = Principal
- r = Annual interest rate in decimal form
- n = Number of compounding periods per year
- t = Time in years
Compound interest is:
CI = A − P
For annual compounding, the formula can be simplified to:
A = P(1 + r)^t
Simple Interest vs Compound Interest Example
Suppose ₹10,000 is invested at 10% per year for 10 years.
Under Simple Interest
SI = ₹10,000 × 10 × 10 / 100
SI = ₹10,000
Final amount:
₹20,000
Under Compound Interest
If the interest is compounded annually:
A = ₹10,000 × (1 + 0.10)^10
The final amount is approximately:
₹25,937
So, under these assumptions, compound interest produces approximately ₹5,937 more than simple interest.
RBI gives a similar illustration showing how compounding can produce substantially more growth over a 10-year period. Its example uses quarterly compounding at 10%, resulting in ₹26,851 compared with ₹20,000 under simple interest.
Key Differences Between Simple and Compound Interest
| Factor | Simple Interest | Compound Interest |
| Calculation base | Original principal | Principal plus accumulated interest |
| Interest earned on previous interest | No | Yes |
| Growth | Consistent interest amount | Increasing interest amount |
| Long-term effect | Usually smaller | Can be significantly larger |
| Compounding frequency | Not applicable | Annual, quarterly, monthly, etc. |
| Calculation | Easier | More complex |
| Benefit to investors | Lower at the same rate and period | Higher potential growth |
| Effect on unpaid debt | Depends on product terms | Can increase outstanding amount through accumulated interest |
Why Does Compound Interest Grow Faster?
The major reason is that the interest itself becomes part of the amount earning future interest.
Consider an investment of ₹10,000 at 10% annual compounding:
| Year | Starting Amount | Interest | Ending Amount |
| 1 | ₹10,000 | ₹1,000 | ₹11,000 |
| 2 | ₹11,000 | ₹1,100 | ₹12,100 |
| 3 | ₹12,100 | ₹1,210 | ₹13,310 |
| 4 | ₹13,310 | ₹1,331 | ₹14,641 |
| 5 | ₹14,641 | ₹1,464 | ₹16,105 |
The interest amount increases each year because the balance keeps increasing.
How Does Compounding Frequency Affect Returns?
Compound interest may be calculated at different frequencies, such as:
- Annually
- Half-yearly
- Quarterly
- Monthly
When the nominal annual rate is the same, more frequent compounding can result in a higher final amount because interest is added to the balance more often.
However, you should always check the actual rate, effective return and terms of the financial product rather than comparing only the stated interest rate.
Simple Interest vs Compound Interest for Investments
For investors, compounding can be beneficial because accumulated returns can generate further returns.
This becomes particularly important over longer periods. RBI’s financial education material recommends starting savings or investments early and continuing regularly to make better use of compounding.
For example, a person who leaves returns invested for many years may experience significantly greater growth than someone who repeatedly withdraws those returns.
Actual investment returns, however, depend on the financial product and are not guaranteed simply because the concept of compounding applies.
Simple Interest vs Compound Interest for Loans
The effect can be different for borrowers.
If interest is added to an outstanding debt under the applicable terms, future interest may be calculated on a larger amount. This can increase the cost of borrowing.
RBI specifically notes that compounding can work against borrowers when debt remains unpaid.
It is therefore important to understand whether a loan uses simple interest, reducing-balance calculations, or another applicable interest method. Many common bank loans do not simply use a basic flat simple-interest calculation.
Which Is Better: Simple or Compound Interest?
There is no universal answer because it depends on whether you are earning interest or paying it, as well as the specific terms.
For an investment, compounding can increase the potential accumulated amount over time.
For debt, accumulated interest can increase the amount owed if payments are not made as required.
Therefore, instead of looking only at the words “simple” or “compound,” compare the actual interest rate, calculation method, compounding frequency, fees and other terms.
FAQs
What is the main difference between simple and compound interest?
Simple interest is calculated on the original principal, while compound interest considers the principal plus accumulated interest.
Which grows faster, simple or compound interest?
At the same rate and over the same period, compound interest generally produces a higher amount because previously earned interest also earns interest.
Is compound interest always better?
Not necessarily. It can benefit savings and investments, but compounding can also increase the cost of certain unpaid debts.
What is the simple interest formula?
The formula is:
SI = P × R × T / 100
What is the compound interest formula?
The general formula for the final amount is:
A = P(1 + r/n)^(nt)
Compound interest is then calculated by subtracting the principal from the final amount.
Does compound interest depend on time?
Yes. The effect of compounding generally becomes more significant as the investment remains invested for a longer period.
Conclusion
The difference between simple interest and compound interest is mainly how interest is calculated. Simple interest remains based on the original principal, while compound interest allows accumulated interest to become part of the amount earning future interest.
For long-term savings and investments, compounding can significantly increase growth. For borrowing, understanding how interest is calculated can help you estimate the actual cost of debt and avoid surprises.
