How does compound interest work?

Compound interest works by adding the interest earned in each period to the principal. Future interest calculations are then based on this increased principal, allowing for faster growth over time.

What is the formula for compound interest?

The formula for compound interest is A = P (1 + r/n)^(nt), where A is the final amount, P is the initial principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

How often is interest compounded?

Interest can be compounded annually, semi-annually, quarterly, monthly, or daily. The more frequently interest is compounded, the greater the impact on growth.

What are the benefits of compound interest?

Compound interest allows investments to grow exponentially over time. The longer you leave your money invested, the more it compounds, making it a powerful tool for long-term savings.

What is the difference between simple and compound interest?

Simple interest is calculated only on the original principal, while compound interest is calculated on both the principal and the accumulated interest. Compound interest results in faster growth.

Compound Interest: How It Works & Why It Matters

Compound interest

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 (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.

Good for

•

Building long-term wealth:

Compound interest accelerates growth by reinvesting earnings over time.

•

Maximising early saving:

The sooner you start, the more time your money has to compound.

•

Earning interest on interest:

Returns grow exponentially as interest accumulates on past gains.

Things to consider

•

Compounding takes time:

The biggest gains happen later, so patience is key.

•

Debt compounds too:

High-interest debt can grow quickly, working against savings.

•

Returns aren't guaranteed:

Investment growth varies, and market downturns can slow compounding.

1. What is compound interest?

Compound interest is the interest calculated on the initial 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.

2. Compound interest formula

Compound interest is calculated using a formula that accounts for the initial , 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:

A = P ( 1 + r n ) ^nt

Where:

A = Final amount (principal + interest)

P = Initial, or principal amount

r = Annual interest rate

n = Number of times interest is compounded per year

t = Time, in years

3. Benefits of compounded interest

Compounded interest strengthens your investment growth and reduces the effort needed to reach your financial goals, making it a powerful tool for building wealth.

Accelerated growth: - Compounded returns build on themselves, causing your investment to grow faster as it expands.
Easier goal achievement: - Compounding reduces the amount you need to save or invest by making your money work harder for you.

4. Downsides of compound interest

Although compound interest is a powerful tool for growing wealth, it can also work against you when borrowing. Here are the main risks to be aware of:

Debt acceleration: - Compound interest can cause debts to grow rapidly, especially with credit cards or loans where interest compounds frequently, making it harder to pay off balances over time.
Lost growth opportunities: - Money spent servicing compounding debts cannot be used for saving or investing, limiting your potential to build wealth elsewhere.

5. 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, the growth might seem slow, but as the years progress, the interest starts compounding on the previously earned interest, leading to exponential growth.
Longer time frames mean greater growth: - The more time you allow for your investments to grow, the larger the balance will be. Time allows the compound effect to fully take hold, turning small contributions into significant amounts.
Starting early pays off: - Even small investments made early in life can grow significantly over time, thanks to the power of compounding. It's not about how much you save initially, but how long you let it grow.
The impact of compound interest is exponential: - As your investment grows larger, the interest earned each year increases, creating a snowball effect that can dramatically boost your savings.

To fully harness the power of compound interest, it's crucial to start saving or investing as early as possible and to allow your money time to grow. The longer your time horizon, the more impactful the compounding effect will be.

6. How compound interest differs from simple interest

Unlike compound interest, simple interest is calculated solely on the original investment or loan amount. It does not take into account the accumulated interest over time. As a result, simple interest leads to slower growth because the interest is earned only on the , not on previously earned interest.

Formula: The formula for calculating simple interest is:

i = P × r × t

Where:

i = Simple interest

P = Principal (initial investment or loan amount)

r = Annual interest rate (as a decimal)

t = Time (in years)

Example: If you invest £1,000 at an interest rate of 5% for 5 years, the simple interest would be £250 (£1,000 × 0.05 × 5). This would bring the total amount after 5 years to £1,250.

By contrast: If the same investment were calculated using the compound interest method, with interest compounded annually, the result would be £1,276.28. This difference arises because compound interest allows interest to accumulate on both the principal and the previously earned interest, resulting in faster growth over time.

7. Simple v compound interest calculator

As we can see from the calculator above, the frequency at which interest is compounded plays a critical role in determining the total amount of interest earned or paid. Compounding can occur annually, semi-annually, quarterly, monthly, or even daily. The more frequently the interest is compounded, the higher the overall return or cost.

Annual compounding: - Interest is calculated and added to the principalPrincipal is the original amount of money borrowed or saved, before interest. once a year. This is the simplest form of compounding.
Quarterly or monthly compounding: - Interest is added more frequently (every three months or monthly), resulting in faster accumulation compared to annual compounding.
Daily compounding: - Interest is calculated and added every day, which maximises growth. This method is more commonly used in credit cards or loans, where it can increase the cost of borrowing.

Calculator

Simple interest calculator

Use our calculator to explore how compounding frequency impacts the and the total interest paid on your savings.

Balance:

Gross or nominal rate:

Compound frequency:

Years:

FUTURE BALANCE:

INTEREST:

ANNUAL EQUIVALENT RATE (AER):

Interpreting the result

8. Impact of compound interest on your savings

Let's explore how your initial investment grows over time, breaking down the total interest into the amount earned directly on your and the amount earned from reinvested interest.

Your initial investment (£):

ANNUAL EQUIVALENT RATE (AER):

Show years: