Tools

Paying a Premium Monthly, as an Annual Rate

A quotation prints the cost of paying a premium monthly as a percentage of the whole premium. What is it as an annual rate on the money actually borrowed?

Paying an annual premium in instalments is borrowing the unpaid part of it from the insurer. The quotation prices that credit as a percentage of the whole premium — and you only owe the whole premium at the very start, because every instalment reduces it. Divide the same cost by what you actually owed and the figure is substantially larger, often around twice as large. This page does that division from four numbers on your own quotation, and prints the two figures side by side.

What this tool does not decide

Whether to pay monthly. Paying monthly buys something real: the annual sum stays in your hands. This page prices that and does not say whether it is worth paying for.
Who to insure with. This tool names no insurer, broker, product or cover type, ships no list of quotes and fetches none. The evidence that qualified it is that a restatement is missing, and that supports publishing the restatement — not a recommendation.
What the arrangement really costs. Four numbers cannot capture an arrangement fee, a set-up charge, a tax difference between the two ways of paying or a mid-term adjustment, and every one of those makes the true rate higher than the figure here. They are listed in the methodology rather than summarised away.
Whether this is the APR. It is not. A regulated APR includes charges this page does not know about, so a figure here is generally lower than an APR for the same arrangement rather than higher.
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 quotation, in four numbers

Four figures, all printed on the quotation in front of you. Nothing is sent anywhere, nothing is stored, and no insurer, product or market rate is looked up. There is no field for the rate, because the rate is what these four figures already imply.

The premium if you pay in one go

The single-payment price for the same cover, as the quotation states it. This is what the monthly arrangement is measured against: without it there is no comparison and nothing being financed.

What you pay at the start

The first payment, taken before the instalments begin. Enter 0 where the arrangement takes twelve equal instalments and nothing up front. A larger initial payment means less is financed, which lowers the cost in money and generally raises the rate on what is left.

Each monthly instalment

The level monthly amount taken after the initial payment. Enter the instalment itself rather than the total: the total is what the quotation adds up for you, and the instalment is what the arithmetic needs.

How many instalments

How many monthly payments follow the initial one. Ten after a deposit and twelve with none are both ordinary. Between 1 and 60 — beyond five years this is not an instalment arrangement on a one-year cover.

Result

Paying an annual premium in instalments is borrowing the unpaid part of it from the insurer, and the uplift on the quotation is not the rate you are borrowing at. The uplift is divided by the whole premium — but you do not owe the whole premium for most of the year. Every instalment reduces what is outstanding, so the amount you have actually borrowed, averaged over the term, is roughly half the premium. A cost divided by twice the balance it was charged on produces a figure roughly half the true rate, which is why the number on the quotation and the number this page publishes are so far apart.

Enter your four 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.

What you pay in total, spread across the year: Not yet calculated
What paying monthly costs you, in money: Not yet calculated
The uplift as the quotation states it, against the whole premium: Not yet calculated
What the insurer is left waiting for, at the start: Not yet calculated
What you actually owed on average, across the instalment months: 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 instalments discount at: Not yet calculated
How many times the printed uplift the annual rate actually is: Not yet calculated

The rates here 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 credit agreement’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. Neither is an APR in the regulated sense: an APR includes charges this page does not know about, so a figure here will generally be lower than an APR quoted for the same arrangement rather than higher.

This is arithmetic on four numbers printed on a quotation: the single-payment premium, what is paid at the start, each monthly instalment and how many there are. It assumes the instalments are level, that the first falls one month after the initial payment, and that nothing else is added along the way. It contains no arrangement fee, no set-up charge, no insurance premium tax difference between the two ways of paying, no mid-term adjustment, no cancellation and no default.

A rate is not a verdict. Paying monthly buys something real: the annual sum stays in your hands and stays available for whatever else the year brings. This page prices that, and does not say whether it is worth paying for. For a household that would otherwise borrow the annual premium somewhere more expensive, or go without cover, a high implied rate can still be the right arrangement — and nothing here decides that for you.

How this is worked out

Why the figure on the quotation is not the rate

A quotation that offers the premium in one payment or in instalments, and prints the difference as a percentage, is not quoting you a rate. It is dividing the extra you pay by thewhole premium — and the whole premium is a balance you owe for about a month.Every instalment reduces what is outstanding, so the amount you have actually borrowed, averaged over the term, is roughly half of it. A cost divided by twice the balance it was charged on comes out at roughly half the rate.

Three quantities, and what each one is divided by. The middle column is why the first row and the last row are not the same number twice.
Quantity	For example	What it measures	Divided by	Time in it
The uplift on the quotation	8%	Extra paid, per unit of the whole premium	The whole premium, which you owe only at the very start	None at all
What you actually owed	About half the premium	Money	It is the balance	Averaged across the instalment months
The implied annual rate	17% a year	Cost, per unit outstanding, per year	What was outstanding at each point, month by month	A year

What is actually outstanding, month by month

Take the simplest arrangement — twelve equal instalments, nothing paid up front — and follow what you owe:

At the start: The whole premium is outstanding
Halfway through: About half of it is
Before the last instalment: Roughly one twelfth is
Averaged across the year: A little over half the premium — not the premium

That is the whole mechanism, and the result above publishes the average exactly rather than approximately. The approximation is an explanation and not a calculation: an arrangement with a large deposit and few instalments has an average balance nowhere near half the premium, and its rate is correspondingly further from twice the printed figure.

The identity the rate is solved from

What the insurer is left waiting for is the premium less whatever you pay at the start. The implied monthly rate is the i at which your instalments discount back to exactly that:

F = A − D            F = M × 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. The two annual figures are then 12 × i, which is how a credit agreement'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 this is not an APR

An APR in the regulated sense includes charges this page does not know about — an arrangement fee, a set-up charge, a difference in tax between the two ways of paying. Every one of those makes the true cost higher, soa figure here will generally be lower than an APR quoted for the same arrangement rather than higher. If a quotation states an APR, that figure is the more complete one and this page's job is finished: it exists for the arrangements that state a percentage uplift and no rate at all.

What you enter

Four figures, and all four are printed on the quotation: the single-payment premium, what is paid at the start, each monthly instalment, and how many there are. There is no field for the rate, because the rate is what those four imply. There is no field for an insurer, a product or a cover type, because none of them changes the arithmetic.

The limits this conversion imposes on itself

The instalments are level and the first falls one month after the initial payment. A quotation whose instalments vary describes a different arrangement.
The premium and the instalments are in the same unit, and every rate is invariant in it.
The rate is found by a search that verifies its own answer against the identity rather than returning the last value it tried.
Where the instalments total exactly the single-payment premium, the rate is exactly zero and is reported in words rather than as a number.
Nothing here is conditional on any insurer, broker, product or cover type, and no figure below describes a market.

What is not modelled

any arrangement, set-up or credit fee charged on top of the instalments
a difference in insurance premium tax between paying annually and paying monthly
a mid-term adjustment, which changes the premium and the schedule together
cancelling part-way through, and what is then owed or refunded
missing an instalment, and any charge or lapse of cover that follows
the interest the annual sum would have earned if it had been kept back instead
the identity of any insurer, broker, product or cover type
tax, in any jurisdiction

The mechanism behind the comparison — why two uses of money can only be held against each other once they are expressed on the same basis — is taught in the explainer:how to compare two financial uses of money.

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 puts an instalment quotation on the basis a rate is quoted on; 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: Instalment Premium Rate v1.0
Last reviewed: 27 August 2026
The printed uplift: The extra you pay, divided by the whole premium. It has no time in it and it is measured against a balance you owe only at the start, which is why it is not a rate and cannot be compared with one
The implied rate: The rate at which the instalments discount back to what was actually financed. It is measured against a balance that falls with every payment, which is what makes it several times the printed figure
What is financed: The premium less whatever is paid at the start. It is what the insurer is left waiting for, and it is the only balance credit could be charged on
The schedule: Level and monthly, with the first instalment one month after the initial payment. An arrangement whose instalments vary is a different one and is not modelled
Nominal: Twelve times the monthly rate. The convention a credit agreement’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
Not an APR: A regulated APR includes charges this page does not know about. A figure here will generally be lower than an APR quoted for the same arrangement rather than higher
The unit: Unspecified, and the answer does not depend on it. Every amount is in the same unit and every rate is invariant in it
Instalments totalling exactly the premium: Answered in closed form at exactly zero rather than searched. A rate of four parts in ten thousand million million published as the cost of a free arrangement would be a worse answer than none
Excluded: Arrangement and set-up fees, tax differences between the two ways of paying, mid-term adjustments, cancellation and default
Rounding: Display only; intermediate values remain unrounded

Correction history

The specification that ordered this model described the mean outstanding balance as about half the premium and used that approximation to argue the factor of two. The implementation publishes the mean balance exactly rather than approximately, and the difference matters at the edges: an arrangement with a large deposit and few instalments has a mean balance nowhere near half the premium, and the understatement factor there is correspondingly far from two. The approximation survives as an explanation and does not survive as a calculation.
The arrangement in which the instalments total exactly the single-payment premium 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 charges nothing for the credit 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.