The formula behind compound interest is simpler than it looks. Here it is broken down step by step, with worked examples in pounds sterling.
A = P(1 + r/n)nt
This single formula calculates how money grows when interest compounds over time. It looks intimidating at first glance, but each letter represents a simple concept. Let us break it down.
The total value of your investment at the end of the period — your original money plus all compound interest earned. This is what you are solving for.
Your initial deposit or starting balance. This is the amount you invest at the beginning. For example, a £5,000 lump sum.
The yearly rate of return expressed as a decimal. For 7%, use 0.07. For 5%, use 0.05. This is the nominal annual rate, not the effective rate.
How many times per year interest is calculated and added to the balance. Annual = 1, quarterly = 4, monthly = 12, daily = 365. Most UK savings accounts compound daily or annually.
The number of years you leave the money invested. This is the most powerful variable — doubling the time more than doubles the total interest earned.
Let us use a realistic UK example. You invest £5,000 into a Stocks & Shares ISA earning 7% per year, compounded annually, and leave it untouched for 10 years.
Step 1: Identify the values
P
£5,000
r
0.07
n
1
t
10
Step 2: Plug into the formula
A = 5000 (1 + 0.07/1)1 x 10
A = 5000 (1.07)10
A = 5000 x 1.96715...
Result
A = £9,835.76
Your £5,000 has nearly doubled — earning £4,835.76 in compound interest alone
How often interest compounds affects the final result. More frequent compounding means interest starts earning its own interest sooner. Here is the same £5,000 at 7% for 10 years, but with different compounding frequencies:
| Compounding | n value | Final amount | Interest earned |
|---|---|---|---|
| Annually | 1 | £9,835.76 | £4,835.76 |
| Quarterly | 4 | £9,971.29 | £4,971.29 |
| Monthly | 12 | £10,048.31 | £5,048.31 |
| Daily | 365 | £10,068.76 | £5,068.76 |
The difference between annual and daily compounding on £5,000 over 10 years is about £233. That is real money, but it is far less dramatic than the difference made by the interest rate itself or the time horizon. For most practical purposes, the compounding frequency matters less than how much you invest, at what rate, and for how long.
Most UK savings accounts compound daily or annually. Stocks & Shares ISA returns effectively compound continuously as share prices move daily. The formula still provides an excellent approximation.
Most people do not invest a single lump sum and walk away. They add money every month. The formula for compound interest with regular contributions is more complex:
A = P(1 + r/n)nt + PMT x [((1 + r/n)nt - 1) / (r/n)]
Here, PMT is the amount you add each compounding period (for example, £200 per month if n = 12). The first part of the formula calculates the growth on your initial lump sum. The second part calculates the growth on all your regular contributions.
Example: £5,000 initial deposit plus £200 per month at 7% compounded monthly for 10 years:
The contributions formula is genuinely difficult to calculate by hand. This is exactly why tools like our compound interest calculator exist — you enter your numbers and it handles the maths instantly.
If you prefer a spreadsheet, both Excel and Google Sheets have a built-in function called FV (Future Value) that handles compound interest for you. The syntax is:
// Excel / Google Sheets formula
=FV(rate, nper, pmt, pv)
// Example: £5,000 at 7%, monthly compounding, £200/month, 10 years
=FV(0.07/12, 12*10, -200, -5000)
// Returns: £44,354
The parameters are:
The negative signs on pmt and pv are an Excel convention — they indicate cash flowing out of your pocket into the investment.
Understanding the formula is valuable — it helps you grasp why compound interest is so powerful and which variables matter most (spoiler: time and rate of return dwarf everything else). But for day-to-day financial planning, there is no need to punch numbers into a calculator.
Our compound interest calculator lets you enter your starting balance, monthly contribution, expected return, and time horizon — and instantly see a detailed year-by-year breakdown with interactive charts. It handles monthly compounding, contribution timing, and even accounts for different compounding frequencies.
Try the formula with your own numbers — no maths required.
Open compound interest calculatorOpen a free Stocks & Shares ISA and start compounding from just £1. Zero commission, FCA regulated, and all growth is tax-free inside the ISA wrapper.
Capital at risk. This is not financial advice. Affiliate link — we may earn a commission at no extra cost to you.
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