Tools

Repayment Multiple as an Annual Rate

An arrangement quotes a multiple rather than a rate — repay 1.4 times what you take. What is that as an annual rate, and what does the answer depend on?

A price quoted as a multiple cannot be compared against a price quoted as a rate, and the reason is not presentation. A multiple states money repaid per unit advanced and contains no time at all; a rate states money per unit advanced per year. What connects them is the term — and the quote does not contain one either. This page derives the term from what you repay each month, converts the multiple on it, and shows you what happens to the answer when only the repayment changes.

What this tool does not decide

Whether to take the arrangement. A rate is something to compare against your own alternatives, not a verdict on an offer.
Who to borrow from. This tool names no provider, product or arrangement type, ships no list of offers and fetches none. The evidence that qualified it is a regulator documenting a comparison gap, and that supports publishing a conversion — not a recommendation.
What the arrangement really costs. Three numbers cannot capture a fee, a revenue-linked repayment, a staged drawdown or an early settlement, and every one of those makes the true rate higher than the figure here. They are listed in the methodology rather than summarised away.
Which annual convention you should be using. Both are published, and a comparison against a quoted rate whose own compounding basis you do not know is the same mistake one step further along.
Anything about tax, in any jurisdiction.

Your figures

The interactive calculation runs in your browser and needs local JavaScript, which is currently switched off. Activating the Calculate button does nothing at all: no request is sent and nothing is submitted.

Everything else on this page works without it. The model, the formulas, the timing convention, the worked example, the assumptions and the limitations are all in the methodology below, and the companion explainer covers the mechanism in full.

The arrangement, in three numbers

Three figures, all yours. Nothing is sent anywhere, nothing is stored, and no provider, product or market rate is looked up. There is no field for how long the arrangement lasts, because that is the one thing this page works out for you — and it is what the annual rate depends on.

What you receive

The amount advanced to you, before anything is repaid. Neither annual rate depends on how large it is — halve it and halve the monthly repayment and every rate below is unchanged — so use whatever unit the quote is in.

The quoted multiple

The factor the arrangement quotes: 1.4 means you repay 1.4 times what you take. Enter it as a factor and not as a percentage — 1.4, not 40. It is a quantity of money per unit advanced, and it contains no time at all, which is why it cannot be compared against anything quoted per year until this page attaches a term to it.

What you repay each month

The level monthly amount that settles the total. This is the control that decides the answer: the same multiple settled faster costs the same money over less time, which is a higher annual rate. Change it after your first calculation and watch the rate move while the cost does not.

Result

A multiple is not a rate, and the difference is not a matter of presentation. “Repay 1.4 times what you take” states an amount of money for every unit advanced, and says nothing at all about time. An annual rate states an amount for every unit advanced per year. Moving between the two needs the term — how long the money is actually outstanding — and the quote does not contain one. This page derives the term from what you repay each month, and every rate below is conditional on that derivation rather than on the multiple alone.

Enter your three figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

The multiple you were quoted, as a factor: Not yet calculated
What you repay in total: Not yet calculated
What the arrangement costs, in money: Not yet calculated
How long it takes to settle, at that monthly repayment: Not yet calculated
As an annual rate, nominal — 12 times the monthly rate: Not yet calculated
As an annual rate, effective — the monthly rate compounded twelve times: Not yet calculated
The monthly rate the repayments discount at: Not yet calculated

These rates are comparable with a rate quoted on the same basis, and with nothing else. The nominal figure is twelve times the monthly rate, which is the convention a lender’s note rate is usually quoted in; the effective figure compounds that monthly rate twelve times, which is the convention this site’s investment models use. They are two different numbers describing one arrangement. Comparing either against a quoted rate whose own compounding basis you do not know is the same mistake as comparing a multiple against a rate, one step further along.

This is arithmetic on three numbers: what you receive, what you repay in total, and what you repay each month. It assumes the repayment is level and continues until the total is settled, and it treats the final part-month as a part-month rather than rounding it up to a whole one. It contains no fee, no drawdown schedule, no revenue path, no early settlement, no default and no product.

A rate is not a verdict. This page converts a price into a unit you can compare; it does not say whether the arrangement is worth taking, whether a cheaper one exists, or who offers one. A high implied rate on money outstanding for four months can be the right thing to accept, and a low one over six years can be the wrong thing, and nothing here decides that for you.

How this is worked out

Why a multiple cannot be compared against a rate

A quote of repay 1.4 times what you take and a quote of 12% a year are not two prices in different formats. They are two different kinds of quantity, and no amount of rearrangement turns one into the other on its own.What separates them is time, and the quote does not contain any.

Three quantities, and what each one can honestly be compared against. The middle two columns are why the first row and the last row are not rivals.
Quantity	For example	What it measures	Time in it	Comparable with
A quoted multiple	1.4	Money repaid, per unit advanced	None at all	Only with another multiple settled over the same term
The implied term	20.00 months	Time	It is the time	Only with another term
An annual rate	41.32% a year, nominal	Money, per unit advanced, per year	One year, by construction	With another rate quoted on the same compounding basis

Where the term comes from, since you did not enter one

The arrangement produces it. The term is the total repayable divided by the monthly repayment — you repay a total of M × A at R a month, so it is settled after:

n = M × A ÷ R

That figure is generally not a whole number of months, and it is deliberately not rounded to one: the last payment is a part-payment, and rounding the term up would move the published rate by up to a month's worth of cost. It is also the reason there is no control for the term. A reader who could type one would be able to state a length of time the arrangement does not have, and receive a rate for it.

The identity the rate is solved from

The implied monthly rate is the i at which the monthly repayments discount back to the advance:

A = R × a(n, i)        a(n, i) = (1 − (1 + i)^−n) ÷ i

There is no closed form for i, so it is found by a search that verifies its own answer against the identity above rather than returning the last value it tried. The two annual figures are then 12 × i, which is how a lender's note rate is usually quoted, and(1 + i)^12 − 1, which is how this site's investment models compound. Both are published, and neither is called "the annual rate" anywhere on this page.

Why the rate moves when the repayment moves

The cost in money is fixed by the multiple: M × A − A, and nothing about the repayment schedule changes it. What the repayment changes is how long that cost is spread over. A cost of 20,000 borne for seven months and the same 20,000 borne for twenty-eight months are the same money and very different prices, and a rate is the only unit that says so.That is why a multiple is not a rate: the same multiple is several rates, and which one it is depends on a number the quote leaves out.

An advance of 50,000 at a quoted multiple of 1.4, settled at three different monthly repayments. The multiple is the same in every row. So is the cost. The rate is not.
Repaid each month	Term it implies	Cost in money	Annual rate, nominal
1,750.00	40.00 months	20,000.00	21.05%
3,500.00	20.00 months	20,000.00	41.32%
7,000.00	10.00 months	20,000.00	79.65%

A reader told only "1.4×" has been told the third column and nothing else. The calculator above builds this same table from your own figures, so you can see the flat cost and the moving rate in the arrangement you were actually quoted.

What you enter

What you receive: The advance. Neither annual rate depends on its size
The quoted multiple: A factor of 1 or more, entered as a factor and not as a percentage
What you repay each month: A level monthly amount. This is what decides the term, and therefore the rate

The limits this conversion imposes on itself

Three numbers cannot describe an arrangement completely, and every one of these makes the true rate higher than the figure above rather than lower. A converted price published without them would be a stronger claim than the arithmetic supports.

Any charge levied on top of the multiple — an arrangement fee, a draw fee, a servicing charge — is outside this arithmetic. A fee raises the true cost and therefore the true rate, and this page will report the lower figure.
The repayment is assumed level and monthly. Several arrangements quoted as a multiple settle out of a share of revenue instead, so the term moves with trading and the single rate below is one point on a range.
The advance is assumed drawn in full at the start. Drawing it in instalments shortens the average time the money is outstanding and raises the implied rate.
Early settlement is not modelled, and whether the multiple is reduced when you settle early is the single largest thing this arithmetic cannot see. Where it is not reduced, settling early raises the implied rate sharply.
The final month is treated as a part-month. An arrangement that requires a whole final payment costs marginally more than this reports.
Nothing here is conditional on any provider, product or arrangement type, and no figure below describes a market.

What is not modelled

any charge on top of the multiple — an arrangement fee, a draw fee or a servicing charge
a repayment that varies with revenue, which is how several arrangements quoted this way actually settle
drawing the advance in instalments rather than all at once
settling early, and whether the multiple is reduced when you do
missing a payment, defaulting, and any consequence of either
security, guarantees, and what is pledged against the advance
the identity of any provider, product or arrangement type
tax, in any jurisdiction

Two uses of money are only comparable once they are expressed on the same basis, which is this question with the basis named.The explainer on comparing two financial uses of money covers that one, and needs no JavaScript at all.

Go deeper

The nearest published mechanism
How to Compare Two Uses of Money Without Fake Certainty
Why opportunity cost only exists relative to a real alternative, what makes a comparison like-for-like, why a higher annual rate can start behind, and why the option that ends higher is not automatically the one to choose.
Two uses of money are only comparable once they are expressed on the same basis. This page attaches a term to a multiple so that it can be; the explainer is about why the basis has to be named at all.
Read the explainer: How to Compare Two Uses of Money Without Fake Certainty

Calculation model and corrections

Calculation model: Implied Rate v1.0
Last reviewed: 27 August 2026
The multiple: A factor, not a rate. It states money repaid per unit advanced and carries no time at all, which is why it cannot be compared against anything quoted per year until a term is attached
The term: Derived, never entered. It is the total repayable divided by the monthly repayment, so the arrangement produces it and you do not choose it
The last month: A part-month, and kept as one. Rounding the term up to a whole month would move the published rate by up to a month of cost
The repayment: Level, monthly, and continuing until the total is settled. A repayment that varies with revenue is a different arrangement and is not modelled
Nominal: Twelve times the monthly rate. The convention a lender’s note rate is usually quoted in
Effective: The monthly rate compounded twelve times. The convention this site’s investment models use. It is the larger of the two and it is not a different arrangement
The unit: Unspecified, and the answer does not depend on it. The advance and the repayment are in the same unit and every rate is invariant in it
A multiple of exactly one: Answered in closed form at exactly zero rather than searched. A rate of four times ten to the minus seventeen published as the cost of a free arrangement would be a worse answer than none
Excluded: Fees, drawdown schedules, revenue paths, early settlement, default and tax
Rounding: Display only; intermediate values remain unrounded

Correction history

The specification that ordered this model expected it to require a change to the shared monotonic solver, and warned that such a change would carry a parity obligation over every existing calculator on the site. It did not require one. Both obstacles that specification named — that the term is derived rather than supplied, and that it is generally not a whole number of months — turned out to be properties of the objective rather than of the solver, and the third, that a present value falls as a rate rises, cost one minus sign. The shared primitive was left untouched and the finding was recorded as a finding rather than as an absence.
A multiple of exactly one was originally left to the numerical search, which returned a rate a few parts in ten thousand million million above zero. That is arithmetically defensible and editorially wrong: an arrangement that repays exactly what it advanced costs nothing, and a page publishing a positive rate for it would be describing a cost that does not exist. The state is now answered in closed form and reported in words rather than as a number.