banking.savings-aer

export function savingsAer(grossRateBasisPoints: number, paymentsPerYear: number): number

import { savingsAer } from "#fune/banking.savings-aer@^1";

/**
 * The AER of a gross rate paid `paymentsPerYear` times a year:
 * (1 + i / n)^n − 1, per the UK Finance / BSA AER Practice Note formula (d),
 * rounded half-up to two decimal places of a percent (a whole basis point).
 *
 * With i = b / 10000 and D = 10000 × n the exact value in basis points is
 * 10000 × ((D + b)^n − D^n) / D^n, computed in integers and rounded once.
 */
export function savingsAer(grossRateBasisPoints: number, paymentsPerYear: number): number {
  if (!Number.isInteger(grossRateBasisPoints) || grossRateBasisPoints < 0 || grossRateBasisPoints > 100000) {
    throw new RangeError(`grossRateBasisPoints must be between 0 and 100000, received ${grossRateBasisPoints}`);
  }
  if (!Number.isInteger(paymentsPerYear) || paymentsPerYear < 1 || paymentsPerYear > 365) {
    throw new RangeError(`paymentsPerYear must be between 1 and 365, received ${paymentsPerYear}`);
  }
  const n = BigInt(paymentsPerYear);
  const d = 10000n * n;
  const whole = d ** n;
  const numerator = 10000n * ((d + BigInt(grossRateBasisPoints)) ** n - whole);
  // Half-up for a non-negative fraction: floor((2N + M) / 2M).
  return Number((2n * numerator + whole) / (2n * whole));
}

Install

fune build

With that line in your source, in a TypeScript project (language typescript in fune.project), fune build resolves it and its 1 dependency, pins them in fune.lock, downloads only the TypeScript package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. Or pin a range in fune.project and build in one step:

fune add banking.savings-aer

The manifest, vectors and README with only the TypeScript implementation. Install it without the registry with fune add ./banking.savings-aer-1.0.0-typescript.fune, or fetch it from a terminal with fune pull banking.savings-aer@1.0.0:typescript.

The whole function, every language, is one file too: banking.savings-aer-1.0.0.fune, 9,250 bytes, sha256 c56d71d3e9015670eff51ce4aa5368744bbd1301c9d9d60a8e5fbb287083612e. It installs into a project of any language.

// fune: before banking.savings-aer

// fune: after banking.savings-aer

// fune: replace math.big-integer in banking.savings-aer

// fune: step banking.savings-aer after <n|label>

More from the author

The UK Finance / Building Societies Association "Annual Equivalent Rate (AER) Practice Note" (January 2025, which replaced the 1985-2024 "Code of Conduct for the Advertising of Interest Bearing Accounts" and its AER appendix) gives, where interest is paid more often than annually, formula (d):

AER = ((1 + i / (n × 100))^n − 1) × 100

with i the gross annual rate in percent and n the number of times a year it is paid. Guideline A5: "AERs are to be rounded and displayed up to two decimal places." Its worked example 5: 5.8% paid monthly is 5.956...%, an AER of 5.96%; worked example 1: interest paid once a year has an AER equal to the gross rate. Both are vectors here.

Source: https://www.ukfinance.org.uk/policy-and-guidance/guidance/annual-equivalent-rate-aer-practice-note (PDF: https://www.ukfinance.org.uk/system/files/2025-02/Annual%20Equivalent%20Rate%20AER%20practice%20note_0.pdf), read 2026-09-23.

## Exact, then rounded once

The rate is b basis points, so with D = 10000 × n the AER in basis points is exactly 10000 × ((D + b)^n − D^n) / D^n. That is computed in integers (`bigint`, Python `int`, `math.big-integer` in Rust; for daily interest D^n has about 2,400 digits) and rounded half-up to a whole basis point, which is two decimal places of a percent. "Rounded" in A5 is read as the usual half-up; there is no floating-point step where 4.595% could become 4.5949999%.

## What it does not do

The Practice Note's general formula (a) also covers bonuses, rates that step up, deposits during the term and terms other than a year; those need the cash flows and an iterative solve, and are not this function. This is the fixed-rate, whole-year, single-deposit case of formula (d), which is what a headline AER almost always is. The rate is gross (before tax), 0 to 100000 basis points, and interest is paid 1 to 365 times a year.

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