Interest rates are only comparable when they compound on the same schedule. A rate of 5% compounded twice a year is not the same as 5% compounded monthly — but there is a monthly rate that is exactly the same. This calculator finds it. Enter a rate and its compounding frequency, choose the frequency you need, and get the equivalent nominal rate along with the rate per period and the effective annual rate both share.
How to use the equivalent interest rate calculator
- Enter the nominal annual rate you have.
- Choose how that rate is compounded now.
- Choose the compounding frequency to convert to.
- Read the equivalent rate and the rate per period, and use the table to see the same rate at every frequency.
Equivalent rate formula
Both rates must give the same effective annual rate:
Solving for the new rate:
With continuous compounding on either side, the effective rate is er − 1 and the continuous rate is ln(1 + EAR).
Worked example
A mortgage is quoted at 5% compounded semi-annually, with monthly payments. What monthly-compounded rate is equivalent?
Effective annual rate: (1 + 0.05/2)2 − 1 = 5.0625%
Monthly rate: (1.025)2/12 − 1 = 0.412392%
Equivalent nominal rate: 12 × 0.412392% = 4.9487% compounded monthly
On a $300,000 mortgage over 25 years, using the correct 0.412392% monthly rate gives a payment of $1,744.81. Simply dividing 5% by 12 would overstate it at $1,753.77 — almost $9 a month too high.
Another example: 6% compounded monthly equals 6.0301% compounded quarterly, since both are 6.1678% effective.
5% compounded semi-annually at every frequency
| Compounding | Equivalent nominal rate | Rate per period |
|---|---|---|
| Annually | 5.0625% | 5.0625% |
| Semi-annually | 5.0000% | 2.5000% |
| Quarterly | 4.9691% | 1.2423% |
| Monthly | 4.9487% | 0.4124% |
| Weekly | 4.9409% | 0.0950% |
| Daily | 4.9389% | 0.0135% |
More frequent compounding needs a slightly lower stated rate to reach the same yield; less frequent compounding needs a higher one.
When to convert rates
Payments on a different schedule than compounding
Whenever payments happen more or less often than interest compounds — semi-annual compounding with monthly payments, or monthly compounding with bi-weekly payments — the per-payment rate must come from an equivalent rate, not simple division. The advanced loan calculator does this automatically, and the periodic interest rate calculator shows the per-payment rate directly.
Comparing offers quoted differently
A savings account at 4.9% compounded daily and a bond fund at 5% compounded annually can be compared once both are expressed with the same frequency, or as effective rates with the effective annual rate calculator.
These are exact conversions. Check your loan or deposit agreement for the compounding convention it actually uses.
Frequently asked questions
What is an equivalent interest rate?
Two nominal rates are equivalent when they produce the same effective annual rate despite compounding at different frequencies. For example, 5% compounded semi-annually and 4.9487% compounded monthly both grow money by 5.0625% a year.
How do I convert a rate from one compounding frequency to another?
Use r2 = m2 × [(1 + r1/m1)^(m1/m2) − 1], where r1 is the original rate compounded m1 times a year and m2 is the new frequency. Equivalently, convert the first rate to an effective annual rate, then convert that to a nominal rate at the new frequency.
Why do Canadian mortgage calculations need this?
Canada's Interest Act requires fixed-rate mortgage rates to be stated with yearly or half-yearly compounding, and lenders conventionally use semi-annual compounding. Payments are usually monthly, so the quoted rate must be converted to an equivalent monthly rate before the payment can be calculated.
Does converting the rate change how much interest I pay?
No. An equivalent rate is just another way of writing the same cost or yield. What changes the interest is changing the effective rate, not the way it is expressed.