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Interest rate converter
Two percent a month is not twenty-four percent a year — it is 26.82%. This converts a rate between every way it can be quoted: per period or per year, nominal or effective, flat or reducing balance, before or after inflation. No loan details needed for the first one.
The rate you have
A yearly headline is the periodic rate multiplied out and nothing more. An effective rate already has the compounding in it, which is why the two differ.
How often interest is added to the balance. This is the setting that decides the whole answer.
Only affects daily rates. A daily quote means nothing until you say which year it was divided by, and commercial lending often divides by 360.
In money, if it helps
Optional. Prices one year on this balance both ways, so the gap between the two rates stops being abstract.
Effective annual rate
26.82%
Nominal annual rate 24.00%
Compounding adds 2.82% a year on top of the headline.
- Equivalent per day
- 0.0651%
- Nominal annual
- 24.00%
- Continuously compounded
- 23.76%
- Effective annual
- 26.82%
One year on this balance
- At the nominal rate
- ZAR 2,400.00
- At the effective rate
- ZAR 2,682.42
- What compounding adds
- ZAR 282.42
An estimate for pricing and for explaining a quote. Your loan agreement, your local disclosure rules and your own rounding decide what has to be published.
The same rate, quoted eight ways
Every line below costs exactly the same over a year. Only the compounding frequency changes — which is why a quoted rate means nothing until you know the frequency attached to it.
Opens in Excel, Sheets or any spreadsheet.
| # | Compounded | Times a year | Rate per period | Nominal annual |
|---|---|---|---|---|
| 1 | Day | 365 | 0.0651% | 23.77% |
| 2 | Week | 52 | 0.458% | 23.82% |
| 3 | Fortnight | 26 | 0.9182% | 23.87% |
| 4 | Month | 12 | 2.00% | 24.00% |
| 5 | Quarter | 4 | 6.1208% | 24.48% |
| 6 | Six months | 2 | 12.6162% | 25.23% |
| 7 | Year | 1 | 26.8242% | 26.82% |
| 8 | Continuously | — | — | 23.76% |
Why one rate has so many faces
Nothing here is a trick of arithmetic. Each of these is a different question about the same money, and quoting the answer to one as though it answered another is where most rate disputes begin.
- 1
Nominal is a label, effective is a cost
A nominal annual rate is just the periodic rate multiplied by the number of periods — 2% a month written as 24% a year. It ignores the fact that the second month charges interest on the first month's interest. The effective rate puts that back in, which is why it is the only figure two loans can honestly be compared on.
- 2
Frequency is the whole difference
24% compounded once a year is 24%. Compounded monthly it is 26.82%; daily, 27.11%. The quote never changes and the cost does. Any rate given without the compounding frequency beside it is incomplete, and the gap widens the higher the rate goes.
- 3
Which year you divide by
A daily rate is an annual rate divided by the days in a year, and there is more than one answer to how many that is. Actual/365 is the common retail convention; commercial and short-term lending frequently uses 360, which makes each day slightly more expensive. Neither is wrong, but the two are not interchangeable.
- 4
The rate nobody quotes
Lending at 18% while inflation runs at 6% is not an 18% return, and it is not 12% either — it is 11.32%. The exact relation divides rather than subtracts, and the shortcut drifts further from the truth the higher inflation climbs. In a volatile currency it is the only rate that tells you whether the book is growing.
Eight quotes, one identical cost
A lender quoting 2% a month could publish any of the annual figures below and be telling the truth. All eight describe the same 26.82% effective annual cost — the only thing that changes is how often the interest is added to the balance.
| Compounded | What it means | Nominal annual quote |
|---|---|---|
| Daily | Interest added every day. Standard for overdrafts, revolving credit and penalty interest, and the frequency where the day-count convention starts to matter. | 23.77% |
| Weekly | Common in short-term and microfinance lending, where instalments fall weekly and interest is added on the same rhythm. | 23.82% |
| Fortnightly | Follows a fortnightly payroll, which is why it turns up in salary-backed and employer-deducted lending. | 23.87% |
| Monthly | The default nearly everywhere, and the source of the confusion this page exists for: the 24% here is the same cost as the 26.82% at the bottom. | 24.00% |
| Quarterly | Usual on business facilities and term loans with quarterly reviews, where interest is capitalised four times a year. | 24.48% |
| Every six months | Bond and long-term facility convention. Interest is added twice, so the annual quote has to be higher to reach the same cost. | 25.23% |
| Yearly | Compounded once, so the nominal quote and the effective rate are the same number. This is the only row where the headline is honest without a footnote. | 26.82% |
| Continuously | The mathematical limit, used in pricing models rather than in loan agreements. It is the lowest quote of the eight because it compounds constantly. | 23.76% |
Read the column top to bottom: the more often interest is added, the lower the annual quote needs to be to arrive at the same place. Comparing two lenders on the nominal figure alone compares nothing at all.
Effective Interest Rate (EIR/APR) CalculatorQuestions about converting interest rates
- There are two answers and they are both correct. Multiply by twelve for the nominal annual rate: 2% a month is 24% a year. Compound it for the effective annual rate: 1.02 to the twelfth power, less one, is 26.82%. The first is what most lenders publish; the second is what the borrower pays. If you are comparing offers, use the second.
- Only as a headline. The cost is 26.82% a year, because each month charges interest on the interest already added. The 2.82 percentage point difference is the compounding, and it grows with the rate — at 5% a month the nominal 60% is really 79.59%.
- A nominal rate is a periodic rate multiplied out to a year with the compounding ignored. An effective rate is what a year genuinely costs with the compounding counted. They are equal only when interest is added exactly once a year. Every other frequency makes the effective rate the larger of the two.
- Usually not, though the terms are used loosely. In most disclosure regimes APR is a nominal annual rate — the periodic rate multiplied by the number of periods — with mandatory fees folded into it. The effective annual rate compounds instead of multiplying and often excludes fees. Two lenders can quote the same APR and charge different amounts, which is why the effective figure is worth calculating separately.
- Because interest that has already been added starts earning interest itself. The more often that happens, the more of it there is. Going from annual to monthly compounding on a 24% quote adds 2.82 percentage points of real cost without a single term of the loan changing.
- Whichever your agreement says, and it needs to say one. Actual/365 is the common retail convention. Commercial, trade and short-term lending frequently uses 360, which makes each individual day about 1.4% more expensive than the same annual rate divided by 365. The difference is small per day and material over a portfolio.
- It is the limit of compounding more and more often, and it turns up in option pricing and risk models rather than in loan agreements. It is included here because academic and treasury figures are often quoted that way, and converting them to something a borrower would recognise is otherwise fiddly.
- The return left after inflation. Divide one plus the nominal rate by one plus inflation and subtract one — at 18% with 6% inflation that is 11.32%, not the 12% that simple subtraction suggests. Where inflation is high or volatile, the real rate is the only figure that says whether a loan book is actually growing in value.
- No. The whole calculation runs in your browser, and the exports are generated on your own device. Nothing you type is sent to a server, saved, or logged, and there is no sign-up.
How do I convert a monthly interest rate to an annual one?
Is 2% a month the same as 24% a year?
What is the difference between nominal and effective interest?
Is APR the same as the effective annual rate?
Why does the compounding frequency change the rate?
Should a daily rate use a 365 or a 360 day year?
What is continuous compounding for?
What is a real interest rate?
Is my data stored?
Quote one rate, charge exactly that
Lendbox holds the rate, the compounding frequency and the day-count convention on the product itself, then applies them to every loan written against it — so the figure in the agreement, the figure on the schedule and the figure the borrower pays are the same figure.
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