Convert an annual interest rate into an equivalent compound rate and a simple proportional rate per month, quarter, week or day. Enter your values; the result updates as you type, with the method shown below.
About this calculator
An annual rate can be split into a monthly, quarterly or half-yearly rate in two ways: the equivalent (compound) rate, which gives back the annual rate when compounded, or the proportional (simple) rate, which is just divided. Lenders and savers do not always use the same one.
Enter the annual rate and the period to convert to. The calculator shows both the equivalent and the proportional rate per period.
When to use it
- Finding the monthly rate of a loan or a savings product.
- Understanding why two banks show different monthly rates.
- Converting rates for a spreadsheet.
- Studying financial mathematics.
How to read the result
Equivalent: (1 + r)^(1/k) − 1; proportional: r / k. At 6% a year, that is 0.487% or 0.5% a month.
Mortgages usually use the proportional rate; the equivalent rate is used for actuarial comparisons and many savings products.
Mistakes to avoid
- Mixing the two methods in one calculation.
- Multiplying a monthly rate by 12 and calling it effective.
- Using the wrong period.
Formula
Equivalent = (1 + r)^(1/k) − 1 Proportional = r / k
Worked example
6% a year: 0.487% a month equivalent, 0.5% proportional.
Frequently asked questions
Equivalent or proportional?
The equivalent rate compounds back to the annual rate; the proportional rate is simply divided.
Which do French loans use?
Mortgages usually use the proportional rate.
Which for savings?
The equivalent rate.
Which one do mortgages use?
In most countries, the proportional rate (annual rate / 12).
Why is the equivalent rate lower?
Because compounding adds interest on interest within the year.
How do I go from monthly to annual?
Effective: (1 + monthly)^12 − 1.
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Results are estimates for information only. Check important figures with a professional.