Compound interest is one of the most powerful concepts in finance. It allows money to grow over time by earning interest not only on the original amount, but also on previously earned interest.
This is often described as “interest on interest”, and it is the reason savings and investments can grow significantly over long periods.
---What Is Compound Interest?
Compound interest means that each time interest is added, it becomes part of the principal for the next calculation.
Unlike simple interest, where interest is calculated only on the original amount, compound interest grows exponentially over time.
---Compound Interest Formula
The standard formula is:
A = P (1 + r/n)nt
Where:
- A = Final amount
- P = Initial principal
- r = Annual interest rate (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
How to Calculate Compound Interest Step by Step
Example 1: Annual Compounding
You invest £1,000 at an interest rate of 5% for 3 years.
Step 1: Convert percentage to decimal.
5% = 0.05
Step 2: Apply the formula.
A = 1000 × (1 + 0.05)3
A = 1000 × (1.1576) = £1,157.63
Total interest earned = £157.63
---Example 2: Monthly Compounding
You invest £1,000 at 5% for 3 years, compounded monthly.
n = 12
A = 1000 × (1 + 0.05/12)36
A ≈ £1,161.62
Monthly compounding gives slightly higher returns because interest is added more frequently.
---Simple vs Compound Interest
Simple interest: calculated only on the original amount
Compound interest: calculated on original amount + accumulated interest
Over time, compound interest grows much faster.
---Why Compound Interest Matters
- It helps savings grow faster
- It increases investment returns
- It also increases debt if applied to loans
The earlier you start, the more powerful compounding becomes.
---How Time Affects Growth
Time is the most important factor in compound interest.
Even small interest rates can produce large gains over long periods.
For example:
- £1,000 at 5% for 5 years ≈ £1,276
- £1,000 at 5% for 20 years ≈ £2,653
Use the Compound Interest Calculator
To calculate compound interest instantly, use our Compound Interest Calculator.
You can also use the Loan Calculator to estimate repayments, or the Percentage Calculator to work with interest rates.
---Common Mistakes
Forgetting to Convert Percentages
Always convert percentages to decimals before using the formula.
Ignoring Compounding Frequency
Monthly, quarterly, and yearly compounding give different results.
Underestimating Time
Short-term growth looks small, but long-term growth is exponential.
---Frequently Asked Questions
What is compound interest?
It is interest calculated on both the original amount and accumulated interest.
What is the compound interest formula?
A = P (1 + r/n)nt
Why is compound interest powerful?
Because it allows exponential growth over time.
Is compound interest good or bad?
It is good for investments but increases the cost of debt.
---Conclusion
Compound interest is a key concept in finance. It allows money to grow over time by reinvesting interest.
The formula may look complex, but the idea is simple: your money earns interest, and then that interest earns more interest.
To calculate it quickly, use the Compound Interest Calculator.