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Compound Interest Formula Explained

If you’ve ever seen A = P(1 + r/n)nt and thought “what does that even mean?”, this guide breaks it down step by step, with examples you can verify in our compound interest calculator.

The standard compound interest formula

A = P(1 + r/n)nt

It looks intimidating, but it’s just “starting amount” multiplied by a growth factor.

What each variable means

Step-by-step example

Say you invest £1,000 at 5% per year, compounded monthly, for 3 years.

That’s: P = 1000, r = 0.05, n = 12, t = 3

Plugging it in:

A = 1000 × (1 + 0.05/12)12×3

Use the calculator to confirm the exact figure and compare monthly vs yearly compounding.

Monthly vs annual compounding

More frequent compounding usually increases the final amount, but the difference is often smaller than people expect at modest interest rates.

ScenarioCompoundingApprox outcome
£1,000 @ 5% for 3 yearsYearly~£1,157.63
£1,000 @ 5% for 3 yearsMonthly~£1,161.47

Continuous compounding

Some finance math uses continuous compounding: A = P ert. It’s a useful model, but most savings accounts and loans compound daily, monthly, or yearly rather than continuously.

Common calculation mistakes

FAQ

What does “n” mean in the compound interest formula?

n is how many times per year interest is added to the balance (e.g. 12 for monthly).

Is compound interest the same as APY?

APY (or AER in the UK) reflects the effect of compounding over a year, so it’s closely related but not the same as a raw annual rate.

How do I calculate compound interest with regular contributions?

Use a calculator that supports contributions (monthly deposits). That’s the easiest way to avoid mistakes.

Next: If you haven’t yet, read What is compound interest? for an intuitive explanation.

Related guides

What is compound interest?Definition, formula, and a quick example. Compound interest formula explainedBreak down the formula with step-by-step examples. Compounding frequency explainedDaily vs monthly vs yearly — and how big the difference is.

What Is Compound Interest?

Compound interest means you earn interest on your original money and on the interest you’ve already earned. Over time, that “interest-on-interest” effect can become the main driver of growth.

Quick takeaway: Compounding rewards time. Small differences in years can matter more than small differences in rate.

Compound interest, in plain English

With simple interest, the interest calculation never changes: it’s based only on the starting balance. With compound interest, the base grows as interest is added. That makes each future interest payment slightly larger than the last.

Example: if you start with £1,000 and earn 5% per year, a simple-interest loan would add £50 each year. With compounding, the first year adds £50, but the second year adds interest on £1,050, the third year on £1,102.50, and so on.

How compounding works step by step

  1. You start with a balance (your principal).
  2. Interest is calculated using a rate (for example, 5% per year).
  3. The interest is added to the balance at the end of each compounding period (monthly, yearly, etc.).
  4. The next period’s interest is calculated using the new (larger) balance.

This is why compounding frequency matters: if interest is added more often, the balance grows a little sooner, which can slightly increase the total.

The compound interest formula

The standard formula for compound growth is:

A = P (1 + r/n)nt

If you’re also adding money regularly (for example, monthly contributions), the math becomes a series. It’s easier to model using a calculator.

Use the compound interest calculator
Include monthly contributions and compare scenarios ›

A real example (with a table)

Let’s say you invest £1,000 at 5% per year and interest is compounded yearly. Here’s how the balance grows:

YearStartInterest (5%)End
1£1,000.00£50.00£1,050.00
2£1,050.00£52.50£1,102.50
3£1,102.50£55.13£1,157.63
4£1,157.63£57.88£1,215.51
5£1,215.51£60.78£1,276.29

Second example: adding money every month

Compounding gets even more powerful when you keep adding to the pot. Here’s a simple scenario: you invest £200/month at 6% per year, compounded monthly.

YearTotal contributedEnd balance
1£2,400.00£2,467.11
2£4,800.00£5,086.39
3£7,200.00£7,867.22
4£9,600.00£10,819.57
5£12,000.00£13,954.01
6£14,400.00£17,281.77
7£16,800.00£20,814.79
8£19,200.00£24,565.71
9£21,600.00£28,547.98
10£24,000.00£32,775.87

Notice how the growth accelerates in later years—the interest is being earned on top of interest.

Notice how the interest grows each year even though the rate stays the same. That’s compounding.

Compound vs simple interest

Simple interest is linear: interest is calculated on the original principal only. Compound interest is exponential-ish: interest is calculated on an increasing balance.

In the short term, they can look similar. Over long periods, the gap becomes meaningful, especially when you add regular contributions.

Does compounding frequency matter?

Yes, but usually less than people think. Monthly compounding beats yearly compounding, but the difference is modest compared with:

If you want to see the difference, set the same principal and rate in the calculator and switch between yearly and monthly compounding.

Why compounding feels slow at first

Early on, most of your balance is principal, so interest is calculated on a small number. As the balance grows, interest becomes a larger and larger part of the total. This is why consistency matters: the “snowball” needs time to form.

Common mistakes to avoid

FAQ

Is compound interest always good?

It’s good for savings and investing, but it also works against you on debt. The concept is neutral: the direction depends on whether the balance is yours or owed.

What’s the difference between interest rate and APY?

The stated interest rate doesn’t include compounding effects. APY (annual percentage yield) reflects compounding over the year, so it’s often the better comparison number.

What’s the best compounding frequency?

More frequent compounding is slightly better for growth. In practice, the difference between monthly and daily compounding is usually small compared with time, contributions, and fees.

How can I calculate compound interest with monthly contributions?

You can use a compound interest calculator that supports contributions and provides a breakdown of contributed money vs earned interest.

Educational content only. Not financial advice.

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Compound vs Simple Interest

Both concepts describe how interest is calculated, but they grow very differently over time. Here’s the plain-English comparison, with a side‑by‑side table and a real example.

Want to see the numbers instantly? Use the compound interest calculator and compare it with the simple interest calculator.

What is simple interest?

Simple interest is calculated only on the original principal (the starting amount). It does not earn interest on previous interest. That makes it easy to understand and predictable.

Typical simple interest formula: Interest = P × r × t

What is compound interest?

Compound interest is calculated on the principal plus the interest that has already been added. In other words, interest earns interest. The longer the time period (and the more frequently it compounds), the bigger the difference becomes.

If you’re new to the idea, start with what compound interest means and then read the compound interest formula explained.

Key differences (side‑by‑side)

Feature Simple interest Compound interest
Interest is calculated onOriginal principal onlyPrincipal + accumulated interest
Growth over timeLinear (steady)Accelerating (snowball effect)
Compounding frequency matters?NoYes (yearly, monthly, daily…)
Best forShort periods, simple loansLong‑term saving & investing
Common inSome personal loans, car loansSavings, investments, credit card debt

Real example comparison

Imagine you invest £10,000 for 10 years at 5% per year, with no extra contributions.

MethodHow it growsApprox total after 10 years
Simple interest£10,000 + (£10,000 × 0.05 × 10)~£15,000
Compound interest (yearly)£10,000 × (1.05)10~£16,288.95

That ~£1,288 difference is purely the “interest on interest” effect. Over 20–30 years, the gap becomes much larger.

Which one grows faster?

For time periods longer than one interest period (for example, multiple years), compound interest almost always wins for growth because each period adds a bit more base to earn on.

The two levers that change the outcome most are:

  • Time (how many years you let it run)
  • Frequency (monthly beats yearly, all else equal)

To test frequency, try your numbers in the calculator and change the compounding schedule.

When banks use each type

Simple interest is often used when lenders want a straightforward calculation and the period is short or the product is structured around simple accrual.

Compound interest is everywhere in savings and investing (where you want growth), and it can also appear in debt products (where you want to avoid letting balances snowball).

Common mistakes

  • Comparing simple vs compound using different rates or time periods.
  • Ignoring compounding frequency (monthly vs yearly).
  • Assuming “5%” means the same thing everywhere (APR vs APY can differ).
  • Forgetting contributions (regular deposits can dominate the outcome).

FAQ

What is the simple interest formula?

Simple interest is typically calculated as Interest = Principal × Rate × Time. Total amount equals principal plus that interest.

Which grows faster: simple or compound interest?

Compound interest grows faster over multiple periods because interest is added to the base and earns interest in later periods.

When is simple interest used?

Simple interest is common for certain short-term loans and products where interest is calculated only on the starting balance.

Is compound interest always better?

For saving and investing over time, compounding is usually better. For debt, compounding can make balances grow faster if you don’t pay it down.

Next: use the compound interest calculator to model your scenario, then compare with simple interest.