Personal finance
Equivalent simple interest rate
Convert a simple rate from one frequency to another while keeping the interest accrued over a year unchanged.
Why the rate has to be converted
Simple interest calculations require consistency between the unit of the period and the unit of the rate: if you count the duration in months, the rate must be monthly. An annual rate applied to a number of months produces a result that is wrong by a factor of twelve, and it is one of the most common mistakes in hand-made financial calculations.
Under simple interest the conversion is proportional, because interest is never capitalised: the interest accrued over a year is simply the sum of the sub-period figures, with no compounding effect. A 12% annual rate therefore corresponds exactly to 1% monthly, 3% quarterly and 4% four-monthly.
This is precisely where the simple regime parts ways with the compound one: with capitalisation, 12% a year is equivalent to 0.9489% a month, not 1%, because twelve capitalisations at 1% would reach 12.68%. Applying the proportional conversion to a compound-interest contract always overstates the return or the cost.
Example: a loan carrying 6% annual simple late-payment interest, delayed by four months, accrues at the equivalent four-monthly rate of 2%. On a €5,000 debt that is €100 of late interest, computed directly without going through a fraction of a year.
Common mistakes
- Applying this proportional conversion to a compound-interest operation: that case needs the exponential equivalent compound rate formula.
- Swapping source and target period: the source period is the one your rate already refers to, not the one you want to obtain.
- Mistaking the resulting periodic rate for the APR of a loan, which also includes fees and charges on top of interest.
Frequently asked questions
How is a simple interest rate converted?
Multiply the rate by the number of source periods in a year and divide by the number of target periods: i_target = i_source × n_source / n_target. The relationship is purely proportional.
What is a 12% annual rate worth per month?
Under simple interest it is exactly 1% monthly, because interest is not capitalised. Under compound interest it would be 0.9489% monthly instead.
Why do the equivalent simple and compound rates differ?
Because with compound interest each period's interest is added to the capital and earns interest in turn. Reaching the same yearly amount therefore requires a lower periodic rate than a plain division would suggest.
How this calculation works
i_target = i_source × n_source / n_target, where n is the number of periods in a year (12 monthly, 4 quarterly, 3 four-monthly, 1 annual). From 12% annual to monthly: 12 × 1 / 12 = 1%.