What is a periodic interest rate?

It is the rate applied in one period rather than over a year. A nominal annual rate of 6 percent charged monthly is 0.5 percent a month, and that 0.5 percent is what appears on a monthly statement and what a monthly compounding step uses. The relationship is a division: the annual rate divided by the number of periods in the year. Regulation Z defines the periodic rate as a rate of finance charge imposed on a balance for a day, week, month, or other subdivision of a year, which is exactly what this page computes.

How do I calculate the periodic interest rate?

Divide the nominal annual rate by the number of periods per year. At 6 percent a year the monthly periodic rate is 6 ÷ 12 = 0.5 percent, the quarterly rate is 6 ÷ 4 = 1.5 percent, and the daily rate is 6 ÷ 365 = 0.01644 percent. The number of periods is the divisor and nothing else is involved — there is no equation to solve, because the annual rate being a nominal one already means the split is a straight division.

Why is the effective annual rate higher than the nominal rate?

Because the periodic rate compounds. Half a percent a month is 0.5 percent of the balance in the first month, but by the twelfth month the interest from the earlier months is itself earning interest, so a year of it comes to 6.16778 percent rather than 6 percent. The shorter the period, the bigger the gap: at 6 percent the monthly split gives an effective 6.168 percent and the daily split gives 6.183 percent. The effective annual rate is the only one of the two that tells you what a year in the account is actually worth.

Which one should I compare against my statement?

The periodic rate, if you are checking that the interest charged matches the rate you were quoted — loan and credit disclosures are built on the linear split, so a monthly statement should show 0.5 percent on a 6 percent annual rate. The effective annual rate is the right figure when you are comparing what two accounts pay or two loans cost, because it is the only one that accounts for how often the money compounds, and two accounts quoting the same annual rate with different compounding do not pay the same amount.

Does it matter whether interest compounds monthly or daily?

It moves the answer, though not by much at ordinary rates. On 6 percent a year, monthly compounding gives an effective 6.168 percent and daily compounding gives 6.183 percent — about a sixtieth of a percentage point, which is small but real and free to check. The gap widens with the rate: at a nominal 100 percent the monthly split has an effective rate of 161.304 percent and the daily split 171.457 percent, because at that level the compounding is doing as much work as the rate.

Is the periodic rate the same as the APR?

Not quite. The annual percentage rate is an annualised disclosed figure that includes fees as well as interest, and under Regulation Z it is derived from the periodic rate by multiplying that rate by the number of unit-periods in a year. So the periodic rate is the input and the annual percentage rate is the annualised output — this page computes the first and, in its effective annual rate, a different annualisation that accounts for compounding. Neither of them adds fees, and a disclosed rate would.

Periodic Interest Rate Calculator

Result

0.50000%

Periodic interest rate

Effective annual rate (APY, %): 6.168%
Periods of this length in a year: 12

A nominal annual rate is a per-year figure, and almost nothing in finance is actually charged per year. A card quoting 18 percent charges it monthly, a savings account quoting 6 percent may credit it daily, and a bond paying semiannually does so twice. This page performs the split: it takes one nominal annual rate and one compounding frequency and returns the periodic interest rate that is actually applied each period, which is a single division — 6 percent a year paid monthly is 0.5 percent a month. The second figure on the panel is the one that makes the split worth looking at. Splitting a rate linearly is not the same as asking what a year of that compounding actually earns, and the two answers differ: 0.5 percent a month compounded twelve times does not return 6 percent over the year, it returns 6.16778 percent. That gap is not an error in either number. The first is the nominal annual rate divided evenly, which is the convention that loan and card disclosures are built on, and the second is the effective annual rate, which is what actually lands in the account. Seeing them side by side is the whole point: the shorter the period, the smaller each rate and the larger the year. Split 6 percent into 365 daily periods and the daily rate is 0.01644 percent, while the year compounds to 6.183 percent — a third of the linear answer, added on top. The reference table holds the annual rate fixed at 6 percent and walks the frequency from annual down to daily, so the two columns move in opposite directions on the same screen.

6% a year, split five ways — from one period a year to 365

Periods per year	Periodic rate	Effective annual rate
1	6	6
2	3	6.09
4	1.5	6.136
12	0.5	6.168
365	0.01644	6.183

The first column is how many times the year is divided, which is also the divisor applied to the 6 percent: one period a year leaves the rate untouched at 6, twelve periods make it 0.5 a month, and 365 make it 0.01644 a day. The two rate columns move in opposite directions, and that is the single idea this table exists to show. Go down the periodic rate column and the numbers fall by a factor of 365 as the period shrinks; go down the effective annual rate column and they rise, from 6 to 6.183, because a smaller rate applied more often earns more. The distance between the two columns is the cost of the convention: at one period a year they are the same number, and by 365 periods a year the year has gained 0.183 of a percentage point that the nominal 6 percent does not mention. The 12 row is the calculator's default case, and the 365 row is the one that needs five decimal places to show a rate at all.

Formula

Periodic interest rate = nominal annual rate ÷ number of periods per year Effective annual rate = (1 + periodic rate) ^ (periods per year) − 1

Nominal annual rate: The stated annual rate before any splitting — the number quoted on a card, a loan or an account, also called the annual percentage rate when it is the disclosed figure on credit
Periods per year: How many times the year is divided: 1 for annual, 2 for semiannual, 4 for quarterly, 12 for monthly and 365 for daily — this is the divisor, and it is also the number the first column of the reference table lists
Periodic rate: The rate applied in each period, which is what a monthly statement charges and what a monthly compounding step uses — the same annual rate split more finely gives a smaller periodic rate every time
Effective annual rate: What the periodic rate actually earns over a full year once it compounds, which is always at least the nominal rate and grows as the period gets shorter

Use it whenever you have an annual rate and need the number that applies to a period — to check whether the monthly rate a lender quoted really is the annual rate divided by twelve, to turn a quoted annual percentage rate into the rate that will appear on a statement, or to compare two accounts that quote the same annual rate with different compounding. It is also the step that most other calculations quietly do for you: a compound interest page, an annuity page and a mortgage page all split the annual rate internally, so seeing the split on its own is how you find out what those pages assumed. The one thing to be careful about is that this is a nominal split, not an equivalent one. Dividing 6 percent by twelve gives exactly 0.5 percent, and 0.5 percent compounded twelve times gives 6.16778 percent, not 6 percent — both figures are on the panel because both are used, and which one matters depends on the question. Loan and card disclosures are built on the linear split, so if you are checking a statement, the periodic rate is the one to compare against. If you are comparing what two accounts pay, the effective annual rate is the honest one, because it is the only figure that accounts for how often the money compounds.

Worked examples

6% a year charged monthly
1. Periods per year: 12
2. Periodic rate: 6% ÷ 12 = 0.5% a month
3. Effective annual rate: (1.005)¹² − 1 = 6.16778%, printed as 6.168
The default case, and the cleanest place to see the difference between the two figures. Half a percent a month is what the contract charges; 6.168 percent is what a year of it is worth. The 0.168 of a percentage point between them is the compounding, and it is not a rounding artifact — it is the interest on the interest the earlier months earned.
The same 6% credited daily — 0.01644% a day
1. Periods per year: 365
2. Periodic rate: 6% ÷ 365 = 0.016438…% a day, printed as 0.01644
3. Effective annual rate: (1.00016438…)³⁶⁵ − 1 = 6.183%
This is the row that needs five decimal places: at four, the daily rate would print as 0.0164 and the third significant figure would be gone. Compare the effective rate with the monthly case — 6.183 against 6.168 — and you have the entire effect of compounding frequency in two numbers: the same nominal 6 percent pays about 0.015 of a percentage point more when it is credited daily rather than monthly.
18% a year charged monthly — 1.5% a month
1. Periods per year: 12
2. Periodic rate: 18% ÷ 12 = 1.5% a month
3. Effective annual rate: (1.015)¹² − 1 = 19.5618%, printed as 19.562
The magnitude most people meet first, and the reason the effective figure is worth knowing: an 18 percent annual rate charged monthly costs 19.562 percent over a year. The 18 here is an example input chosen to show the arithmetic at a familiar scale, not a claim about what any particular card charges.

Limitations

The split is linear, which is the convention loan and card disclosures use but is not the only one in circulation: an equivalent periodic rate would be (1 + annual rate)^(1 ÷ periods) − 1, and at 6 percent monthly that is 0.4868 percent rather than 0.5 percent. This page gives the linear figure as the periodic rate and the compounded figure as the effective annual rate, and it does not convert between the two conventions — if a document you are checking used the other one, the numbers will not match to the last digit. It assumes the rate is constant for the whole year, so a variable rate, a promotional rate that steps up, or a rate that changes with a central bank decision is outside it. It assumes exactly the stated number of periods with no skipped or partial ones, so an account that credits interest on the actual number of days in each month rather than on a flat 365 will differ slightly, and a rate change partway through cannot be represented. It works on rates, not on money: it will not tell you what a balance earns or costs, because that also depends on the balance itself, on when payments are made and on whether interest is charged on a declining balance or a flat one. The daily setting uses 365 periods, which ignores leap years. Finally, it is not a truth-in-lending calculator and does not implement the annual percentage rate as regulation defines it — it does the one division that figure is built on, and nothing about fees, which the disclosed rate includes and this page does not.

Frequently asked questions

What is a periodic interest rate?: It is the rate applied in one period rather than over a year. A nominal annual rate of 6 percent charged monthly is 0.5 percent a month, and that 0.5 percent is what appears on a monthly statement and what a monthly compounding step uses. The relationship is a division: the annual rate divided by the number of periods in the year. Regulation Z defines the periodic rate as a rate of finance charge imposed on a balance for a day, week, month, or other subdivision of a year, which is exactly what this page computes.
How do I calculate the periodic interest rate?: Divide the nominal annual rate by the number of periods per year. At 6 percent a year the monthly periodic rate is 6 ÷ 12 = 0.5 percent, the quarterly rate is 6 ÷ 4 = 1.5 percent, and the daily rate is 6 ÷ 365 = 0.01644 percent. The number of periods is the divisor and nothing else is involved — there is no equation to solve, because the annual rate being a nominal one already means the split is a straight division.
Why is the effective annual rate higher than the nominal rate?: Because the periodic rate compounds. Half a percent a month is 0.5 percent of the balance in the first month, but by the twelfth month the interest from the earlier months is itself earning interest, so a year of it comes to 6.16778 percent rather than 6 percent. The shorter the period, the bigger the gap: at 6 percent the monthly split gives an effective 6.168 percent and the daily split gives 6.183 percent. The effective annual rate is the only one of the two that tells you what a year in the account is actually worth.
Which one should I compare against my statement?: The periodic rate, if you are checking that the interest charged matches the rate you were quoted — loan and credit disclosures are built on the linear split, so a monthly statement should show 0.5 percent on a 6 percent annual rate. The effective annual rate is the right figure when you are comparing what two accounts pay or two loans cost, because it is the only one that accounts for how often the money compounds, and two accounts quoting the same annual rate with different compounding do not pay the same amount.
Does it matter whether interest compounds monthly or daily?: It moves the answer, though not by much at ordinary rates. On 6 percent a year, monthly compounding gives an effective 6.168 percent and daily compounding gives 6.183 percent — about a sixtieth of a percentage point, which is small but real and free to check. The gap widens with the rate: at a nominal 100 percent the monthly split has an effective rate of 161.304 percent and the daily split 171.457 percent, because at that level the compounding is doing as much work as the rate.
Is the periodic rate the same as the APR?: Not quite. The annual percentage rate is an annualised disclosed figure that includes fees as well as interest, and under Regulation Z it is derived from the periodic rate by multiplying that rate by the number of unit-periods in a year. So the periodic rate is the input and the annual percentage rate is the annualised output — this page computes the first and, in its effective annual rate, a different annualisation that accounts for compounding. Neither of them adds fees, and a disclosed rate would.

References

12 CFR 1026.2(a)(21), Regulation Z — defines the periodic rate as a rate of finance charge that is or may be imposed by a creditor on a balance for a day, week, month, or other subdivision of a year — Consumer Financial Protection Bureau regulation, via the Electronic Code of Federal Regulations (United States)
Appendix J to Part 1026, Annual Percentage Rate Computations for Closed-End Credit Transactions, paragraph (b)(1) General Rule — the annual percentage rate is determined by multiplying the unit-period rate by the number of unit-periods in a year, which is the linear split this page performs — Consumer Financial Protection Bureau regulation, via the Electronic Code of Federal Regulations (United States)
12 CFR 1026.14(c)(1) and its accompanying commentary — the annual percentage rate may be computed by multiplying each periodic rate by the number of periods in the year, or by the quotient method — Consumer Financial Protection Bureau regulation, via the Electronic Code of Federal Regulations (United States)

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Compound Interest CalculatorSee how savings grow with compounding at any frequency.Future Value CalculatorFuture value of a present sum at a given rate.Present Value CalculatorPresent value of a future sum, discounted at a rate.Simple Interest CalculatorInterest earned on a principal without compounding.