How Compound Interest Works

Summary

Compound interest is interest earned on both the original amount (principal) and on previously earned interest. Unlike simple interest — which only grows the original amount — compound interest creates a snowball effect where your money grows faster the longer it’s invested. Combined with regular contributions, compound interest is the primary mechanism behind long-term wealth building.

How it works

The calculator combines two components:

1. Lump-sum growth — your initial deposit grows by earning interest on itself
2. Annuity growth — your regular monthly contributions each earn interest from the point they’re deposited

Contributions are assumed to be made at the end of each compounding period (ordinary annuity convention). Interest is applied first, then the contribution is added — so each contribution starts earning interest from the next period.

Compounding frequency

Interest can compound at different intervals:

More frequent compounding produces slightly higher returns because interest starts earning interest sooner. At typical rates (3–7%), the difference between monthly and annual compounding is roughly 0.1–0.5% per year.

The formula

The first term is the lump-sum growth of the initial principal. The second term is the future value of an ordinary annuity — the accumulated value of all regular contributions with compound interest.

The Rule of 72

A quick mental shortcut: divide 72 by your annual interest rate to estimate how many years it takes for your money to double.

• At 4% → doubles in ~18 years
• At 7% → doubles in ~10 years
• At 10% → doubles in ~7 years

Worked examples

Inputs explained

• Starting amount — the lump sum you’re investing or have already saved (can be £0)
• Monthly contribution — how much you add each month (can be £0 for a one-off lump sum)
• Annual interest rate — the expected annual return. For cash savings, use the AER offered by your bank. For equity investments, 5–7% (after inflation) is a common long-term assumption.
• Time period — how many years the money will be invested
• Compounding frequency — how often interest is applied. Monthly is standard for most UK savings accounts and investment platforms.

Outputs explained

• Final value — the total amount at the end of the period (principal + contributions + all interest earned)
• Total contributions — starting amount plus all monthly contributions over the period
• Total interest — the difference between final value and total contributions — this is the “free” money from compounding
• Interest as % of contributions — shows how much extra you earned relative to what you put in
• Growth chart — stacked area showing contributions (teal) vs interest earned (purple) over time
• Year-by-year table — detailed schedule of balance, contributions, and interest at each year-end

Assumptions & limitations

• Constant rate — the calculator assumes a fixed annual return for the entire period. In reality, returns fluctuate year to year. For equities, the actual annual return might range from −30% to +30%, while the long-term average is ~7% real.
• No fees or taxes — investment fees (e.g. platform charges, fund OCFs) and tax on interest income are not deducted. In a stocks & shares ISA, growth is tax-free; in a general account, interest above the Personal Savings Allowance (£1,000 for basic-rate, £500 for higher-rate taxpayers) is taxable.
• No inflation adjustment — all values are in nominal terms. To see real (inflation-adjusted) growth, subtract expected inflation (~2%) from your rate.
• End-of-period contributions — contributions are assumed to be added at the end of each compounding period (ordinary annuity). If you contribute at the start, actual returns would be slightly higher.

Verification