The Hesapstan compound-to-simple interest rate converter is designed to convert an annual effective compound interest rate into the equivalent annual simple interest rate for a period you choose in days, more clearly. It is built for anyone holding a compound rate who wants to compare it against a simple rate quoted elsewhere: the inputs are the annual effective compound rate, a period in days, and a day-count basis, and the outputs are the effective return for that period and the equivalent annual simple rate. The tool's main limitation is that it assumes the rate you enter is already an annual EFFECTIVE rate — if you hold a nominal rate, convert it to effective first. The result is a mathematical re-expression of one rate as another; it is not investment advice or a market-rate promise.
What this converter computes
You supply a compound rate expressed as an annual effective rate and a period length in days. The calculator first works out the effective return that rate produces over that period, then annualizes that return without compounding to give the equivalent simple rate.
- The effective return for the selected period, as a percentage.
- The equivalent annual simple rate that reproduces the same accumulated value.
- The period length in years, so the day-count fraction actually used is visible.
- The day-count basis applied, stated explicitly in the result.
- No taxes, withholding, fees, inflation, bank terms or market rates.
The calculator does not ask for a compounding frequency, because an effective annual rate already determines growth over any term. If your figure is a nominal annual rate — for example one that compounds monthly — convert it to an effective annual rate before using this tool.
What do simple and compound interest mean?
Under simple interest, the return is always computed on the same original principal; interest earned does not itself earn interest. Under compound interest, each period's interest is added to the principal, and the next period compounds on that larger total.
This tool is not an investment vehicle; it builds a mathematical bridge between two different EXPRESSIONS of interest, letting you compare a compound rate against a simple rate in the same terms.
Why the nominal-versus-effective distinction matters
A nominal annual rate does not by itself determine growth without a stated compounding frequency — a 12% nominal rate compounded monthly produces annual effective growth higher than 12%. The effective rate already incorporates the effect of compounding and states the true annual growth.
If you are not sure whether your figure is nominal or effective, clarify that before using this tool. Entering a nominal rate as if it were effective understates the true growth in the result.
What "equivalent simple rate" means
Two interest rates are equivalent when they produce the same accumulated value over the same term. Simple interest accumulates as 1 + s × t, compound interest as (1 + i)^t. Setting the two equal and solving for s gives s = ((1 + i)^t − 1) / t.
Here t is the period expressed in years — the number of days divided by the day-count basis. The numerator, (1 + i)^t − 1, is the effective return for the period, and dividing it by t annualizes that return on a simple, non-compounded basis, exactly as an add-on rate is quoted in the money market.
When the period is a full year, t equals 1 and the equivalent simple rate comes out identical to the compound rate you entered. That is the quickest way to sanity-check the calculation yourself.
Worked example
Take a 50% annual effective compound rate over 30 days on an ACT/365F basis: t = 30 / 365 = 0.082192 years. Effective return for the period = (1 + 0.50)^0.082192 − 1 = 3.3887%. Equivalent annual simple rate = 3.3887% / 0.082192 = 41.2297% — the same 30-day return, carried to a year without compounding, is 41.2297%, not 50%.
Run the same rate over a full year (365 days) and t = 1, giving an equivalent simple rate of exactly 50% — confirming the full-year identity above.
Why you choose the day-count basis
The day-count basis fixes how many days a year is taken to have, and it genuinely changes the answer. ACT/365F counts the year as 365 days in every year, including leap years; ACT/360 fixes the denominator at 360. Both are standard, widely used conventions.
- ACT/365F: days divided by 365, with the denominator unchanged in leap years.
- ACT/360: days divided by 360, common in short-term money-market lending.
- The same rate over the same days gives different results on the two bases, which is why the basis is selected rather than assumed.
The converter defaults to ACT/365F and names the basis it used in the result. When you compare two figures, make sure both sides are quoted on the same basis.
The risk of comparing rates quoted on different day-count conventions
If a source quotes a simple rate on ACT/360 while you calculate on ACT/365F, the two figures may look comparable but rest on different assumptions. This tool always states which basis it used; you should separately confirm which basis the other figure you are comparing against uses.
41.23% on ACT/365F and 41.23% on ACT/360 look identical but do not represent the same growth. Do not compare a rate quoted with no stated basis directly against this tool's output.
How this differs from the bilesik-faiz compound interest calculator
Hesapstan's bilesik-faiz tool computes how a principal grows over time under compound interest (principal + rate + term + compounding frequency → final amount). This tool answers a different question: given a compound RATE, what simple RATE is equivalent to it over the same term? One computes an amount; the other converts one rate into another.
How to interpret the result
The result is a mathematical re-expression of the compound rate you entered — not investment advice and not a bank or market commitment. Use it to bring two different rate expressions onto the same footing for comparison, not to project future returns.
Which inputs are rejected
The calculator never quietly repairs an ambiguous input. It says the input is invalid and clears the previous result, so a stale or wrong number is never left on screen.
- A period of zero or negative days is rejected: there is no annualized rate over a zero-length period.
- A fractional number of days is rejected, because a day-count convention counts whole days.
- A rate of −100% or below is rejected, because the growth factor would not stay positive.
- Negative rates above −100% are valid and convert normally.
- A rate and period large enough to overflow numerically produce no result at all.
Frequently Asked Questions
What if my rate is not an effective annual rate?
Convert it to an effective annual rate first. A nominal annual rate does not determine growth on its own without a compounding frequency, which is why this tool does not accept one directly.
What is the difference between a nominal and an effective rate?
A nominal rate is the "stated" rate without reference to compounding frequency. An effective rate already incorporates the effect of compounding and reflects true annual growth. This tool only accepts an effective rate.
What is the difference between the two percentages in the result?
The effective return for the period is the return earned over the days you selected. The equivalent annual simple rate is that same return carried up to a year without compounding.
Should I pick ACT/365F or ACT/360?
Pick the basis used by whatever you are comparing against. The difference is large enough to be visible at the precision shown, so two rates are only comparable on the same basis.
Can I directly compare two rates quoted on different day-count bases?
Not safely. The same numeric value can represent different growth on different bases. Convert both rates to the same basis before comparing them.
Is this a projection of investment returns?
No. The tool restates a rate you supply in a different convention. It contains no market rate, no bank product, no tax treatment and no investment advice.
Can I enter a negative interest rate?
Yes. Negative rates above −100% are valid and convert the same way. Values at or below −100% are mathematically undefined here and are refused.