Annual percentage yield from a nominal rate

A nominal rate is a labelling convention, not a yield: it names the slices a year is cut into without saying what those slices do once credited. The APY is what the year actually delivers when every credited slice itself begins compounding. The two coincide only when the year holds a single crediting; at every other frequency the APY sits above the quote.

The gap between nominal and APY grows as either the rate or the frequency rises — but with sharply diminishing effect on the frequency side. Moving a quote from annual to monthly crediting changes the yield noticeably; moving from monthly to daily barely moves it again. An offer advertising its crediting frequency as the lead advantage is usually advertising the smaller half of the story.

Ranking is the whole use. A quote credited monthly and a quote credited quarterly cannot be compared as printed; converted to APY they can, because APY restates both on the identical footing of one undisturbed year. That is why disclosure rules in several markets require an effective figure to be published beside the nominal one — the conversion this page performs is the one those rules exist to force into the open.

The relation also runs in reverse, and the workspace offers that direction for this calculator: name a target APY and it solves for the nominal quote that would deliver it at a given frequency. That direction matters when a competitor advertises an effective figure and the offer in hand states a nominal one — the two can only be weighed after one of them has been walked across to the other’s convention, in whichever direction is shorter.

APY is still a nominal quantity in the inflation sense. It ranks offers in currency terms; it says nothing about what the year’s growth will buy, nothing about tax, and it assumes the interest stays in the account compounding all year. It is the right scale for comparing deposits — and the wrong one for declaring victory over prices.

A nominal quote answers a narrower question than most readers assume. It says how the year is to be sliced and what portion of the annual figure each slice carries — and then stops. What it deliberately does not say is what happens to a slice once it has been credited, which is the interesting part: credited interest joins the balance, and from that moment it earns alongside the principal that produced it. The quote describes the inputs to a year; the yield describes the year.

The conversion is therefore mechanical rather than judgemental. Cut the nominal rate into as many equal slices as the schedule names, let each slice apply to whatever the balance has become, and ask what a full year of that behaviour amounts to as a single annual figure. Nothing is estimated and nothing is assumed about the market; the only facts used are the two the offer already printed.

Because the credited slices compound, the effective figure sits above the quote at every schedule finer than a single yearly crediting — never below it, and never equal to it except in that one case. That direction is not a coincidence of the arithmetic but the whole content of it: the gap between the two numbers is precisely the work the crediting schedule did, and the quote is silent about exactly that work.

It is tempting to read the effective figure as a more generous version of the quote, as though the account were being credited with something extra. Nothing extra is granted. The effective figure is what the same rate produces once the interest it has already paid is allowed to earn as well — interest on interest, and nothing besides. The two numbers describe one account, not two offers.

Splitting the effective yield into those two contributions is a useful habit. One part is the quote itself, which would be the whole story if interest were credited once and left to sit. The other part is everything the schedule added by crediting sooner and letting the credited amounts work. On everyday deposit rates that second part is modest enough to be a footnote; on promotional rates it grows large enough that quoting the nominal figure rather than the effective one starts to look like a decision.

This is also why disclosure rules in several markets require an effective figure to be published beside the nominal one. The rule exists because the second part of that split is invisible in a quote, varies by schedule, and is exactly the part a reader comparing two advertisements needs in order to compare them at all.

Crediting frequency is a favourite line in deposit advertising, and it is the weaker half of the story. Moving a quote from a single yearly crediting to a monthly one moves the yield noticeably. Moving from monthly to daily barely moves it again. The effect is real at every step and it shrinks at every step, so the marketing gain from advertising an unusually fine schedule is almost entirely rhetorical.

The rate is the lever that actually matters. At low rates, even an enormous difference in schedule leaves the effective figures close enough together that the comparison is settled by the quote; at high rates the schedule finally earns real attention, because the slices being compounded are themselves large. An offer leading with its crediting frequency rather than its rate is usually leading with the smaller number.

There is a destination to this shrinking, and it is not a rhetorical one. Push the schedule to its limit — crediting not daily but continuously — and the yield does not run away; it converges on a specific figure that no schedule whatever can pass. That ceiling is a real quantity with its own calculator, and it is where this journey goes next, because knowing the ceiling is how you learn how little of it any real account has left unclaimed.

The effective figure settles one question completely and leaves several open. It ranks offers in currency terms — which account grows a balance faster over an undisturbed year — and it says nothing at all about what that growth will buy. A yield comfortably above another yield can still be a yield below the pace of prices, and the currency figure has no way to show it. That second question is the one the third lesson of this journey answers.

It also assumes the year is undisturbed. Interest credited and then withdrawn stops compounding at the moment it leaves, so a year with movement in it delivers less than the effective figure names. A promotional rate that steps down partway through the year breaks the same assumption from the other side: each phase is its own quote and needs its own conversion rather than one blended guess.

Tax and fees sit outside it too, and they are not small at the margins where two offers are close. The effective yield is the right scale for the comparison it makes, and the discipline it teaches is to know exactly what has been compared — a schedule and a rate, honestly restated — rather than to mistake a clean number for a complete one.

The engine below is the same certified one the calculator page runs — fetched, verified and mounted mid-lesson. It arrives pre-filled with the pack’s own declared example: a promotional-looking quote credited monthly, the kind a teaser certificate leads with. Read the effective figure against the quote first; the distance between them is the lesson. Then re-run the same quote credited quarterly, then once a year, and watch the two figures meet exactly at the single yearly crediting.

Read the result as what one full, undisturbed year at this quote and schedule delivers, in currency terms and before tax. Every figure is computed live by the verified engine as you type; this page stores none, and would rather refuse than estimate.