How compound interest works
Compound interest allows interest to build on earlier interest, accelerating growth over time while also increasing the cost of compounding debt.
In this guide
Compound interest is a powerful financial concept that plays a central role in savings, investments and loans.
It refers to the process by which interest is calculated not only on the initial principal (the original sum of money) but also on the accumulated interest from previous periods. This compounding effect can significantly accelerate the growth of an investment or, conversely, increase the amount owed on a loan over time.
This makes compound interest a cornerstone concept in personal finance, investment strategy and debt management.
Key terms used in this guide6 terms
Definition
Principal
The original amount of money borrowed or saved, before interest.
What is compound interest?
Compound interest is the interest calculated on the initial principal as well as the accumulated interest from previous periods. It is a powerful concept that allows investments or loans to grow exponentially over time as interest is earned on both the original amount and any interest that has already been added.
Unlike simple interest, which is only calculated on the initial original amount, compound interest helps your money grow faster. The more frequently interest is compounded, the greater the overall effect, making compound interest a crucial factor in long-term investments and savings.
Compound interest formula
Compound interest is calculated using a formula that accounts for the initial principal, the interest rate and the frequency with which the interest is compounded. This formula helps you determine how much an investment or loan will grow over time with compound interest.
Formula: The formula for calculating compound interest is:
Where:
- A
- Final amount (principal + interest)
- P
- Initial, or principal amount
- r
- Gross rate
- n
- Number of times interest is compounded per year
- t
- Time, in years
Benefits and downsides of compound interest
Compound interest can help savings grow, but the same effect can make borrowing more expensive. Whether it works for or against you depends on whether you are earning or paying the interest.
Explore both sides
- Growth over time
- Interest can earn further interest, so the amount added may increase as the balance grows.
- Starting earlier
- The longer money remains saved, the more opportunities it has to compound.
- Reaching a goal
- Compounding contributes more of the final balance over longer periods, reducing how much growth must come from new deposits alone.
Time amplifies compounding
Time plays a critical role in how powerful compound interest can become. The longer your money stays saved, the more dramatically it grows, because returns begin to build on top of previous returns, creating an accelerating effect.
In the early years, growth might seem slow and steady. But as time passes, the compounding effect strengthens. Interest earns more interest, and the overall growth curve steepens. Starting early gives you the greatest advantage, allowing even small contributions to grow into significant wealth over the long term.
Compounding accelerates over time
In the early years, growth might seem slow, but as the years progress, interest starts compounding on previously earned interest, leading to exponential growth.
Longer time frames mean greater growth
The more time you allow for your money to grow, the larger the balance can become. Time allows the compound effect to take hold, turning smaller contributions into more significant amounts.
Starting early pays off
Even small amounts saved or invested earlier can grow significantly over time. How long the money has to grow can matter as much as how much you start with.
The impact becomes more pronounced
As the balance grows larger, the interest earned each year increases, which can substantially increase the final balance over longer periods.
To make the most of compound interest, start saving or investing as early as you reasonably can and allow the money time to grow. The longer the time horizon, the more influential the compounding effect can become.
Simple interest formula
Simple interest is calculated only on the original principal. It does not include interest accumulated in earlier periods, so the amount of interest added remains the same when the principal and rate do not change.
Formula: The formula for calculating simple interest is:
Where:
- i
- Simple interest
- P
- Principal (initial investment or loan amount)
- r
- Annual interest rate (as a decimal)
- t
- Time (in years)
How simple and compound interest differ
Simple interest earns interest only on the original balance. Compound interest adds each year's interest to the balance, so the amount earning interest gets larger.
See the effect on £10,000 at 5% over 25 years, compounded annually:
- Your deposit
- Interest on deposit
- Interest on interest
The gap starts in year 2
Both methods earn £500 in year 1. Simple interest then keeps earning £500 a year. Compound interest earns 5% on a growing balance, so the yearly interest rises to £1,612.55 by year 25. By then, interest on interest has added £11,363.55 beyond simple interest.
Simple v compound interest calculator
Explore how your balance grows and how much interest comes from the original principal versus interest already earned. Change the balance, gross rate, compounding frequency and term, then compare the chart and year-by-year breakdown.
For more options, try the standalone advanced calculator.
Inputs
Enter a starting balance, annual rate, compounding frequency and term.
Savings details
Compounding and term
The bottom line
Compound interest becomes more powerful with time because each round of interest increases the balance used to calculate the next one.
Time and rate both matter. Starting earlier gives compounding longer to work, while comparing AER helps you judge savings products on a like-for-like annual basis.
