Compound interest calculator — methodology

The period step

The calculation runs in periods, not years. A period is a month, a quarter or a year, and every step is integer pence arithmetic — there is no floating-point balance drifting over 360 months.

balance ← balance + deposit (if paid at the start of the period)
balance ← balance × (1 + periodic rate)
balance ← balance − charge
balance ← balance + deposit (if paid at the end of the period)

Interest is applied to whatever the balance is at that moment, which is why a deposit paid at the start of a period earns that period’s interest and one paid at the end does not. Over a long term that single period of difference, repeated every period, is worth more than most people expect — and it is a convention, not a fact about money, so the calculator asks rather than assuming.

Interest on interest, which is the whole mechanism

Nothing in the loop above knows how much interest has already been earned. It does not need to: the interest a period adds is a percentage of the balance, and the balance already contains every earlier period’s interest. Compounding is not a separate step, it is what happens when a percentage is applied repeatedly to its own output.

The consequence is the one figure a single-number calculator cannot show you: at a constant rate, the interest credited in a late year is much larger than the interest credited in the first, with nothing about the rate having changed. The year-by-year table on the calculator carries a running interest total beside the deposits so the gap between the two is visible rather than asserted.

Turning an annual rate into a period rate

There are two defensible ways to do this and they do not agree, so the calculator asks which one you mean rather than picking one quietly:

effective (an AER — compounds to the same annual):  periodic = (1 + r)^(1/n) − 1
nominal   (divided across the year's periods):     periodic = r / n

This is what decides whether compounding frequency matters at all. On an effective rate it barely does — n periodic rates compound back to exactly the rate you typed, so monthly and annual compounding differ only by rounding to whole pence. That is not a quirk of this calculator: it is the definition of an AER, which exists so that accounts crediting interest at different intervals can be compared on one figure. On a nominal rate it matters a great deal, because r / n applied n times compounds to more than r.

So “compounded daily” is worth something when the rate quoted alongside it is nominal, and worth almost nothing when it is an AER. A calculator that does not ask which one you have cannot tell you which case you are in.

One period governs three things, and there is no daily option

The engine models a single period type. The interval chosen sets how often interest is added, how often a deposit lands and how often the charge is taken — all three together. Monthly deposits into annually-compounded interest are not expressible, and the page says so rather than offering a second selector that would quietly govern something else.

There is no daily or weekly interval either. A daily schedule over a 30-year term is nearly 11,000 rows, which is a table nobody reads and a page nobody can render honestly; and over decades the answer is dominated by whether the rate assumption holds, not by the interval. Where the interval genuinely changes the answer — a nominal rate — the monthly-against-annual comparison on the calculator already shows the size and direction of the effect.

The charge

A percentage charge is taken off the balance at the point of deduction, at the annual rate divided by the number of periods in the year. It divides nominally because a fee schedule is a tariff rather than a compounding return: “0.25% a year, taken monthly” means one twelfth of 0.25% a month as a matter of the provider’s own terms, and there is no annual figure it has to compound back to.

What a charge costs is never only what it takes. Money deducted in year 2 would have gone on compounding for the rest of the term, so the cost over the term is larger than the charges column — and the calculator reports both figures, because the gap between them is the part that is easy to miss.

A charge levied inside a fund behaves differently: it reduces the return rather than appearing as a deduction, which is where a fund investor actually meets it. That case, along with capped platform fees and flat annual fees, is modelled by the investment calculator.

Rounding, and why the table adds up

Every figure is rounded to whole pence at each period boundary, so each row satisfies opening + deposit + interest − charge = closing exactly rather than approximately. The alternative — carrying fractions and rounding only for display — gives a table whose rows visibly do not add up, which is the one thing a page built to show its working must never do. The price is a drift of a pound or two against the textbook formula over a long schedule.

What it does not model

• Tax of any kind. The balance compounds gross. Interest outside a tax-free wrapper can be taxable depending on your circumstances, and none of that is applied here.
• Rates that change. One rate, every period. A bonus rate that expires after twelve months, a tracker that follows the base rate, and a fixed term ending are all outside the model.
• Inflation. Every figure is in today’s pounds as a nominal amount; nothing is deflated to say what the balance would buy.
• Sequence of returns. If the balance is invested rather than saved, the order the returns arrive in changes the outcome, and a constant rate has no order.