Compound interest calculator

Compound interest is interest earned on interest. Each period, the rate applies to the whole balance, including the interest already added, so growth speeds up the longer the money is left. £10,000 at 5% compounded monthly for 20 years becomes £27,126 with nothing added. Add £250 at the end of every month and it reaches £129,885: £70,000 paid in and £59,885 of growth.

The formulas

A lump sum grows as P × (1 + r/m)^(m × t), where P is the starting amount, r the annual rate, m the number of times a year interest is added and t the number of years. Regular monthly contributions follow the annuity formula, PMT × ((1 + i)^n − 1) / i, where i is the monthly rate and n the number of months. The calculator works month by month rather than using the formulas directly, so it can raise contributions each year and tax each year's interest, but with those options off it matches both formulas to the penny.

Conventions

• Contributions go in at the end of each month and start earning the following month.
• The balance grows each month at the rate that matches the chosen compounding: (1 + r/m)^(m/12) − 1. Daily compounding uses 365 days a year. So 5% compounded yearly gives exactly 5% a year, and 5% compounded daily gives an annual equivalent rate (AER) of 5.13%.
• A yearly increase in contributions applies from the start of each year after the first.
• Each year of the projection is a UK tax year, starting with 2026/27.
• The rate stays the same every year. Real savings rates and investment returns move, so treat the result as an illustration of the effect, not a forecast.

In today's money

With “Show in today's money” on, every figure is divided by the inflation rate compounded over the time to that point, so £129,885 in 20 years at 2% inflation is about £87,409 in today's prices. Each contribution is deflated from the month it's paid, so “paid in” is also in today's money. If inflation is higher than the interest rate, growth shows as a negative number: the savings buy less than what went in.

The ISA switch shows what tax on interest does over time. Inside an ISA, interest is free of income tax. Outside, the calculator treats each year's growth as savings interest, the kind a bank or building society account pays, and taxes it at the end of each tax year:

• The personal savings allowance comes off first: £1,000 for basic-rate taxpayers, £500 for higher-rate and £0 for additional-rate.
• Interest above the allowance is taxed at 20%, 40% or 45% in 2026/27, and at 22%, 42% or 47% from 2027/28, when savings rates rise by 2 percentage points.
• The tax is taken from the balance, as if paid from the savings. In practice it comes through your tax code or Self Assessment, often a year or more later.

On the worked example, a basic-rate taxpayer would pay nothing until 2029/30, when the interest first passes £1,000 a year, and £8,366 in total over 20 years, leaving £118,965 instead of £129,885. At the higher rate it leaves £105,001, and at the additional rate £96,347.

What this leaves out

The calculator assumes nothing else uses up your allowance unless you enter other savings interest, and that your tax band stays the same. In reality, interest counts as income, so a large balance can push you into a higher band and shrink your allowance. The £5,000 starting rate for savings, which only helps people with other income under £17,570, isn't modelled.

Investments outside an ISA are taxed differently: dividends above a £500 allowance at dividend rates, and gains on sale above a £3,000 annual exempt amount at capital gains tax rates. Interest distributions from bond funds are taxed as savings interest. If the money is in shares or funds, the outside-ISA figures here are only a rough guide.

Compound growth is the engine behind most long-term plans. To see how your savings sit alongside property, pensions and debts, try the net worth calculator. To see when your savings could cover your spending, try the FIRE calculator.