Compound interest

Overview

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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.

1. 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 principal, 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 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.

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

Accumulating interest over time can significantly grow your investment, especially when
the interest you earn starts to generate additional interest. This "interest on
interest" effect can accelerate growth, making even small investments valuable over the
long term.

- Interest growth - Over time, the interest you earn starts to grow on itself, helping your savings grow faster.
- Boosting long-term investments - Accumulated interest enhances the growth of long-term investments like retirement accounts, where small contributions grow significantly over decades.
- Starting early pays off - The earlier you invest, the more time your money has to grow. Even small investments grow substantially if left to accumulate over time.
- Reinvestment of earnings - Reinvesting your earnings leads to more growth as the reinvested interest starts earning interest itself.

4. Downsides of compound interest

While compound interest is powerful in growing savings and investments, it can also work
against you in certain situations. Here are some potential downsides:

- Debt growth - Compound interest can cause debt to grow quickly if you are borrowing money. For example, credit card debt or loans that compound interest frequently can make it difficult to pay off balances if you're only making minimum payments.
- High interest rates - When you're paying compound interest on high-interest debt, such as payday loans or certain credit cards, the total amount you owe can snowball and become unmanageable over time.
- Missed payments - Missing payments on loans or debt that accumulate compound interest can cause the amount owed to spiral, making it more difficult to get back on track.
- Opportunity cost - Money that is tied up paying off compound interest on debt is money that could be invested or saved elsewhere, potentially missing out on better growth opportunities.

5. Compound vs simple interest

Simple interest is calculated solely on the principal, or the original investment or
loan amount. Unlike compound interest, 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 principal, not on previously earned interest.

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)

6. Impact of compounding frequency on interest rate

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 principal 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 maximizes growth. This method is more commonly used in credit cards or loans, where it can increase the cost of borrowing.

Calculator:

Try our calculator to explore how compounding frequency impacts the AER or APR. For more
information
read our guide.

Enter gross or nominal rate (%):

Compound frequency:

Annual Rate (AER/APR %):

7. Power of time in compound interest

Compound interest thrives on time, making it a powerful tool for growing your investments or savings. The longer you leave your money invested, the more time compound interest has to work its magic by generating interest not only on the original principal but also on accumulated interest over time.

Time amplifies the benefits of compound interest because the growth becomes exponential rather than linear. The earlier you start saving or investing, the more dramatic the effect of compounding over the years, allowing even modest contributions to grow into substantial amounts.

- 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.

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 principal and the amount earned from
reinvested interest.

Your initial investment (£):

Annual Rate (AER %):

Show years: