Personal finance
Equivalent compound interest rate
Convert a compound rate from one frequency to another while producing exactly the same amount over a year.
Why the conversion is not a division
Two rates are equivalent when, applied to the same capital for the same duration, they produce the same final amount. Under compound interest that condition does not translate into a proportion: each period's interest is added to the capital and earns interest in the next period, so accumulation factors multiply instead of adding up.
The practical consequence is that dividing an annual rate by twelve always overstates the corresponding monthly rate. A 12% annual rate is equivalent to 0.9489% monthly: capitalising twelve times at 1% would reach 12.68% a year, i.e. 68 basis points more than agreed.
This is the distinction between the nominal annual rate, which is simply the periodic rate times the number of periods, and the effective annual rate, which accounts for capitalisation. The more frequent the compounding, the further the two drift apart, and the gap widens as the rate level rises.
Example: a savings account paying 3% a year with quarterly interest credits pays an equivalent quarterly rate of 0.7417%. Anyone using 0.75% (3% ÷ 4) for convenience would end up with a slightly higher amount than actually accrues.
Common mistakes
- Dividing the annual rate by the number of periods: that conversion is valid under simple interest, not under compound interest.
- Swapping nominal and effective rate: the first comes from a proportion, the second accounts for capitalisation and is the only one comparable across different frequencies.
- Converting a rate that is already net of taxes or fees without saying so: comparisons between products must always be made on homogeneous figures.
Frequently asked questions
How is the equivalent compound rate calculated?
With the formula i_target = (1 + i_source)^(n_source / n_target) − 1, where n is the number of periods in a year. The ratio between the two frequencies becomes an exponent, not a divisor.
What is the difference between nominal and effective rate?
The nominal annual rate is the periodic rate multiplied by the number of periods, ignoring capitalisation. The effective rate includes it and is therefore always greater than or equal to the nominal one.
What is a 12% annual rate worth per month?
Under compound interest it is 0.9489% monthly: (1.12)^(1/12) − 1. A 1% monthly rate would instead correspond to an effective annual rate of 12.68%.
Does it also work from monthly to annual?
Yes, the formula works in both directions: set the source period to the one your rate already refers to and the target to the one you want.
How this calculation works
1 + i_target = (1 + 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: (1.12)^(1/12) − 1 = 0.9489%.
Related calculators
Simple interest
Solve for capital, rate, periods or final amount when interest is not capitalised.
Compound interest
Solve for capital, rate, periods or final amount using the compound interest formula.
Equivalent simple rate
Convert a simple rate between monthly, quarterly, four-monthly and annual periods.