What it means
Financial figures arrive in awkward periods: a fund reports a month, a lender quotes a daily charge, a business measures a quarter. Annualising restates all of them as a twelve-month rate, which is the unit most people think in.
There are two ways to do it, and they give different answers. Simple annualisation multiplies the periodic rate by the number of periods; compound annualisation raises one plus the periodic rate to the power of the number of periods, capturing the effect of earnings on earnings.
The compound version is the more accurate description of what actually happens when returns or interest are reinvested or added to the balance. The gap widens as the rate rises, which is why short-term borrowing that looks cheap per week can be startlingly expensive when annualised properly.
Annualised rates should be treated with suspicion when the underlying period is short or unrepresentative. A 4% gain in one strong month annualises to roughly 60%, a number nobody should build a plan around.
The convention also matters in regulated disclosure. Where a lender must quote an annual percentage rate, the calculation method is prescribed so that borrowers can compare products, whereas an internally annualised growth figure has no such discipline and should always be shown with the period it came from.
In practice
Real-world examples.
Example
A treasury team compares a 90-day deposit paying 1.2% for the period with a one-year bond paying 4.6%. Annualising the deposit compound gives roughly 4.89%, so the shorter instrument wins on rate before liquidity is considered.
Example
A subscription business reports 2% month-on-month revenue growth and annualises it to 26.8% rather than 24%, then flags in the board pack that the figure assumes the monthly pace holds for a full year.
Example
An invoice finance provider charges 1.5% per 30 days. A finance director annualises the cost to just under 20% and uses that number to compare the facility against an overdraft quoted at 11%.
Formula
Calculation
Compound annualised rate = (1 + periodic rate) raised to the power of (number of periods per year), minus 1.
Simple annualised rate = periodic rate x number of periods per year.
A portfolio returns 1% in a month. Compounding gives (1.01) to the power of 12, which equals 1.126825, so the annualised rate is 12.68%. Simple annualisation gives 0.01 x 12 = 12.00%, understating the true figure by 0.68 percentage points.
A short-term lender charges 3% for a four-month advance. There are three such periods in a year, so the compound annualised cost is (1.03) to the power of 3, which equals 1.092727, giving 9.27%. Simple annualisation gives 3% x 3 = 9.00%.
On a $250,000 balance, the difference between 9.27% and 9.00% is 0.0027 x $250,000 = $675 a year, which is small here but grows quickly with higher rates and shorter periods.
Shorter periods make the gap much larger. A charge of 1.5% a month looks modest, but compounding it over twelve months gives (1.015) to the power of 12, which equals 1.195618, an annualised cost of 19.56% against the 18.00% that simple multiplication suggests, a difference of about $3,900 a year on the same $250,000 balance.Case study
Seen in the real world.
This is an illustrative and fictional scenario. Ashcombe Tooling, an invented components supplier, was offered a supplier finance facility priced at 1% for every 30 days outstanding, which the sales representative described as very competitive against the company's 13% overdraft.
The finance manager annualised properly. Twelve 30-day periods at 1% compound to (1.01) to the power of 12, which equals 1.126825, an annualised cost of 12.68%. On the company's average $600,000 of financed receivables, that was 0.1268 x $600,000 = $76,080 a year, against 0.13 x $600,000 = $78,000 on the overdraft.
The margin was real but thin, roughly $1,920 a year, and it disappeared once a 0.5% arrangement fee was included. The illustrative lesson was that a per-period rate is not a bargain until it has been annualised on the same basis as the alternative.
Watch out
Common mistakes.
- Using simple annualisation for compounding products, which understates borrowing costs and investment returns.
- Annualising a single short or unusual period, such as one strong trading month, and presenting the result as an expected yearly rate.
- Comparing an annualised internal growth figure with a regulated annual percentage rate as though the two were calculated the same way.
Questions
People also ask.
What is the difference between an annualised rate and an effective annual rate?
The effective annual rate is the compound annualised rate including the effect of compounding within the year, so the two are the same thing when compounding is applied correctly.
Does annualising work for negative periods?
Yes, the same formula applies, and compounding a negative monthly return produces an annualised loss that is smaller in magnitude than simple multiplication suggests.
How many periods make an annualised figure trustworthy?
There is no fixed rule, but a rate built from a full year of observations is far more dependable than one extrapolated from a single month.
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