Wealth Building Basics: How Compound Interest Actually Works

Compound interest: earning money on your money

Compound interest means you earn a return not only on the money you originally invested — the principal — but also on every bit of interest that money has already earned. With simple interest, only the original principal ever earns anything, so growth is a straight line. With compound interest, each period's interest gets folded back into the balance and starts earning its own interest, so growth curves upward and accelerates the longer it runs.

A concrete example: invest £1,000 at 5% compounded annually. Year 1 you earn £50, ending at £1,050. Year 2 you earn interest on £1,050 — £52.50 — ending at £1,102.50. Year 3 you earn £55.13 on the larger balance, ending at £1,157.63. The interest earned keeps rising each year even though the rate never changed, purely because the base it's calculated on keeps growing.

FV = P·(1+r)^n + PMT·(((1+r)^n − 1) / r)

P    = initial investment (principal)
PMT  = monthly contribution
r    = annual rate ÷ 12   (monthly rate)
n    = years × 12          (number of months)

Contributions versus growth: where the money actually comes from

Every pound in a long-term investment account belongs to one of two buckets: money you actually paid in (the principal plus every monthly contribution), or money the account generated on its own through compounding. Early on, contributions dominate the balance — you can watch your own deposits build up almost linearly. But because growth compounds exponentially while contributions only add up in a straight line, the growth bucket eventually catches up and then overtakes the contribution bucket, often by a wide margin over several decades.

Worked example: £10,000 initial investment, £300 a month, at a 7% annual return for 20 years. Total contributed works out to £10,000 + (£300 × 240 months) = £82,000. Run the same numbers through the monthly-compounding formula above and the final balance lands well north of £150,000 — meaning growth alone accounts for a bigger share of the pot than every pound you personally deposited.

The Rule of 72, and why starting early beats a bigger deposit

The Rule of 72 is a mental shortcut for doubling time: divide 72 by your annual percentage return. At 8% interest, money roughly doubles every 9 years (72 ÷ 8 = 9); at 6% it takes about 12 years; at 12% about 6 years. It's an approximation that ignores contributions and exact compounding frequency, but it's accurate enough for quick comparisons between scenarios.

Because compounding is exponential, time in the market is usually worth more than a larger check written later. Someone who invests for 30 years at a modest monthly amount typically ends up ahead of someone who waits 10 years and then tries to catch up with much larger contributions — the first investor's early pounds had a decade of extra compounding that no amount of later saving can fully replace. This is also why diversifying and staying invested through downturns tends to matter more than timing the market: missing the compounding of even a few strong years can meaningfully dent a multi-decade outcome.

Inflation: the reason growth has to outpace the rate quoted

Inflation is the rate at which prices for goods and services rise over time, which means the purchasing power of a fixed sum of money falls. If something costs £10 today and inflation runs at 3% a year, it will likely cost about £10.30 next year. A savings account paying 2% while inflation runs at 3% is technically compounding, but it's still losing real value every year — the account balance goes up, yet it buys less than it used to. That's the core argument for investing rather than only saving: the goal isn't just growth, it's growth that outpaces inflation.

A simple long-term strategy

None of this requires picking winning stocks. A workable long-term approach is: start as early as possible, since time is the one input compounding can't do without; contribute regularly, even in small amounts, since consistent monthly deposits (dollar-cost averaging) smooth out the ups and downs of buying at a single price; diversify across asset classes like stocks, bonds and funds rather than concentrating risk in one place; stay patient through short-term market swings, since the underlying long-term trend is what compounding actually rewards; and reinvest dividends and interest rather than withdrawing them, so every payout immediately rejoins the compounding base instead of sitting idle.

Frequently asked questions

Try it live

Everything above runs in your browser — open Compound Wealth Builder and drag the initial investment, monthly contribution, return rate and time horizon sliders to see contributions and growth split apart on a live chart. Nothing is installed, nothing is uploaded, the whole model lives in one tab.