Compound interest and how savings interest is calculated

Compound interest is the mechanism that makes savings grow faster over time. Halifax defines it plainly: "Compound interest is where you earn interest on the interest you've already earned"¹. In the first year of a savings account, interest is worked out on the money you paid in. Once that interest is added to the balance, the next lot of interest is worked out on the bigger figure, so the same percentage rate produces a slightly larger amount each time it is applied.

The effect is small at first and grows with time. On £1,000 at 5%, the difference between compound and simple interest after two years is just £2.50. After ten years, on a similar example, the difference runs into hundreds of pounds. That widening gap is why providers and guidance sites alike make the same point: the earlier you start saving, the more time compounding has to work².

This page explains how interest is calculated on savings balances, with worked examples at each step, how compound and simple interest differ, what "roll up" interest means, which accounts do not compound at all, and how tax reduces what actually lands in your hands.

Compound interest: earning interest on your interest

An interest rate tells a saver how much money will be paid into their account, as a percentage of their savings, as the Bank of England puts it⁷. What the rate alone does not tell you is what it is applied to. That is where compounding comes in.

With a compound interest account, each time interest is calculated it is worked out on the current balance, which includes all the interest previously added. Halifax's guidance on savings rates explains that with this kind of account "you may be able to grow your funds quicker than if you have an account with simple interest"¹. Its separate guidance on "per annum" rates makes the same point in terms of the balance: "This means that you earn interest on money you deposit as well as any interest you've previously earned"⁸.

The timing matters as much as the principle. Interest can be calculated daily, monthly or annually, and the more often it is calculated and added, the more often the interest itself starts earning. first direct's guidance illustrates this with a savings balance of £1,000 earning £50 over a year when interest is calculated and added yearly³. If the same rate were applied monthly, each month's interest would be added to the balance before the next month's calculation, and the year's total would be slightly higher. The AER figure exists precisely to make accounts with different calculation frequencies comparable, which is covered in interest rates explained.

Principality's savings guidance adds the practical takeaway: "Compound interest can increase your savings over time so the earlier you can start saving, the more time you'll have to earn compound interest"². Nothing about compounding requires a large deposit. It requires time, and a rate that is actually applied to a growing balance.

A worked example: £1,000 at 5%

The clearest way to see compounding is to follow one balance through two years. Principality's worked example starts like this: "If you've got a balance of £1,000 at an interest rate of 5%, after a year you'd have earned £50 of interest"².

Year one: £50 of interest on £1,000

In year one there is nothing yet to compound, because no interest has been added. The rate is applied to the £1,000 you deposited, producing £50 of interest. first direct gives exactly this example, a savings balance of £1,000 with interest calculated yearly earning £50 in the first year³. Its guide to how compound interest works repeats the same first-year figure for a fixed rate savings account paying interest annually⁴.

At the end of year one, the interest is credited to the account. As Principality puts it: "If that interest is added to your savings, you'll have a balance of £1,050"².

Year two: interest on £1,050 brings the balance to £1,102.50

Year two is where compounding appears. The 5% rate is now applied to £1,050 rather than £1,000, so the interest for the year is £52.50 rather than £50. first direct's example continues: "the balance at the end of year 2 could be £1,102.50"³. The extra £2.50 is interest earned on the first year's interest.

Halifax uses a smaller version of the same example in its guidance for teaching children about money: £100 saved at 5% becomes £105 at the end of year one, and by the end of year two "You now have £110.25 from the £100 you saved", made up of the original £100, £5 of interest from each year, and 25p earned on the first year's interest⁹. The proportions are identical to the £1,000 example, which is the point: compounding works the same at any scale.

The balance at the end of each year, with interest added once a year

How compounding builds over longer periods

Two years shows the mechanism but not the payoff. Over longer periods the interest on interest accumulates into sums that surprise people.

Handelsbanken's jargon buster gives a ten-year example: "If you saved £1,000 for 10 years at a fixed rate of 4%, you might think your account balance at the end would be £1,400", but with compounding the balance is £1,480.24⁵. The £80.24 difference is entirely interest earned on earlier interest.

Aviva's compound interest calculator guidance uses a faster rate to make the same point: "let's imagine I invested £1000 and it grew a steady 10% each year", and "After five years with constant 10% interest, my £1000 is now worth about £1600"¹⁰. With simple interest the same deposit would have grown to £1,500, so five years of compounding added roughly £100.

Which?'s guide to offset mortgages shows the effect on savings held over 25 years: £5,000 in savings at 1% would earn £1,419 in interest over 25 years, and £20,000 at the same rate would earn £5,678¹¹. Those figures assume the interest stays in the account and compounds.

The principle extends well beyond savings accounts. Standard Life estimates that "two thirds of the value of a typical pension pot comes from compound investment growth", not from the contributions paid in¹². That is investment growth rather than savings interest, and investments can fall as well as rise, but it shows how much of long-term growth is compounding rather than saving itself.

Regular saving compounds too, though more slowly at first, because each deposit only earns interest from the day it arrives. Which? gives the example of saving £300 a month for 12 months at 7.1%: "you'd earn closer to £137, as each deposit only earns interest for part of the year"¹³.

Compound or simple interest: how each one grows your savings

Simple interest is calculated only on the original deposit, for as long as the money stays in the account. Aviva's example: "if you invest £1,000 at 5% simple interest, you'll earn £50 a year, every year"¹⁰. The interest never joins the balance, so it never earns anything itself.

Compound interest applies the rate to the growing balance instead. Lloyds' guidance illustrates the two side by side: with simple interest, £1,000 saved at 2% gives £1,020 after a year, while a compounding example shows a balance of £1,030 at the end of year one and £1,060.90 at the end of year two¹⁴. The second year's interest is larger than the first because it is worked out on the larger balance.

The same £1,000 at 5%, with interest either paid out or added to the balance

For a saver leaving money untouched in one account, compounding always produces the larger balance, and the gap widens every year. On the £1,000 at 5% example the difference after two years is £2.50³. After ten years at 4%, the difference between compounding and the straight-line figure is £80.24⁵. The choice between the two is rarely one a saver makes directly: it is a feature of how the account is built, which is why the next section matters.

Roll up interest and other names for compounding

"Roll up" is a term that appears on both sides of the fence, savings and borrowing, and it means slightly different things in each.

On savings, roll up interest is interest that is not paid out as it accrues but is held and paid later, often when a fixed term ends. Because the interest sits in the account, it can itself earn interest, depending on the account's terms. Fixed-rate savings bonds work this way: MoneyHelper notes that with them "You usually get a higher interest rate than from instant access savings accounts", and the longer you lock your money in, the higher the rate is likely to be¹⁵. NS&I's Guaranteed Income Bonds give a concrete example: "A £1,000 deposit would earn £94.20 interest by the end of the 2-year term"¹⁶.

On borrowing, roll up interest works against you. Which?'s guide to bridging loans explains: "Interest is charged monthly, but 'rolled up' and repaid in a lump sum at the end, along with the initial loan price and any fees and charges"¹⁷. The FCA's mortgage rulebook defines the interest roll-up mortgage in similar terms, as a type of interest-only mortgage "where no payments of interest or capital are required or anticipated until the mortgage comes to an end"¹⁸. Because nothing is being paid, the interest is added to the debt and then charged interest itself, which is compounding in reverse. Which? makes the consequence explicit for equity release with no repayments: "you end up paying far more than you've borrowed due to the compounding of interest, which could wipe out your property's value entirely"¹⁹.

The same mechanism appears in some government-backed loans. Support for Mortgage Interest, a benefit-related loan to help with mortgage payments, charges compound interest: Age UK explains that "each month's interest is added to your total borrowed amount when the next month's interest is calculated"²⁰. Compounding is neutral: it magnifies whatever it is applied to, a growing savings balance or a growing debt.

Not all savings accounts compound interest

Compounding only happens if interest is added to the balance that future interest is calculated on. Some accounts are designed so it does not.

The clearest case is accounts that pay interest away. NS&I's Income Bonds, for instance, pay interest out monthly to the saver's bank account rather than adding it to the bond balance, so the interest never compounds within the product²¹. The same provider's Guaranteed Income Bonds pay interest at the end of the term¹⁶. Neither is worse or better by design: paying interest away suits someone using the interest as income, while leaving it to compound suits someone growing a pot. Bank of Scotland's guidance illustrates the compounding route: £5,000 saved for 2 years at a fixed interest rate of 2% earns £202 in interest, "bringing your balance to £5,202"²².

Some savings products do not pay interest at all. Credit union savings accounts "either pay interest or a share of any profits", so with a dividend-paying credit union the return arrives as a profit share rather than interest on the balance²³. And Premium Bonds pay prizes rather than interest, so there is no balance growth to compound.

To find out how a particular account handles it, check the summary box. The FCA's rules for savings providers require the summary box to state "The rate or rates of interest that apply to the savings account", along with "the times at which interest payments are calculated and credited"²⁴. That last phrase is the one to look for: it tells you whether interest goes into the account, where it can compound, or out to you. Our guide to reading a savings summary box goes through each row.

Tax can reduce what compounds

Interest you earn is income for tax purposes, and tax on savings interest reduces the amount left to compound. The government's guidance is direct: "You pay tax on any interest over your allowance at your usual rate of Income Tax"⁶.

Most savers pay nothing, because of the personal savings allowance. Which? explains that it "lets basic rate taxpayers earn up to £1,000 in savings interest a year before paying tax"²⁵. Higher-rate taxpayers get a smaller allowance, and additional-rate taxpayers get none at all: "Additional-rate taxpayers don't have a PSA, meaning all their savings interest is subject to income tax"²⁶. Age UK notes that savings in tax-free accounts like ISAs "don't count towards this allowance"²⁷, and the government's ISA rules confirm that "The Personal Savings Allowance does not apply to any growth or interest paid in an ISA", because ISA interest is simply not taxed²⁸. Interest inside an ISA therefore compounds untaxed, which is one reason the cash ISA vs ordinary savings comparison turns on your tax position.

Tax on interest can also arrive after the fact. Which? notes that tax due on savings interest "can be declared on a self-assessment tax return"²⁹, so a saver who crosses their allowance may face a bill later rather than a deduction at source.

For children's savings, a separate rule applies. If interest paid to a child by a parent exceeds £100 from each parent in a year, "all of this interest (not just the amount over £100) will be added to your savings income, and taxed as if it were your own", meaning the parent's³⁰. The details are in our guide to tax on children's savings, and the general rules are in how tax on savings interest works.

Where to get free help

Free, impartial help with savings and interest is available without paying anyone. MoneyHelper, the government-backed money guidance service, publishes plain-English guides to savings products, including fixed-rate bonds and how their interest works¹⁵. For anything to do with tax on interest, HMRC's guidance sets out the allowances and how the tax is collected⁶.

If debt interest, which compounds against you, is the more pressing issue, StepChange is a free debt advice charity whose guidance explains how interest charges build up on borrowing³¹, and Citizens Advice covers the cost of credit, including how interest is added to credit card borrowing³². Both are free, and neither sells financial products.