What it means
Loan and savings rates are usually quoted per year, but interest is rarely charged once a year. A credit card or mortgage adds interest monthly, a bond pays interest twice a year, and some savings accounts credit interest daily.
The periodic rate is the slice of the annual rate that applies to each of those shorter periods. The calculation is a simple division.
An annual rate of 12% charged monthly gives a periodic rate of 12% / 12 = 1% per month, while the same rate charged quarterly gives 3% per quarter. The balance at the start of each period is multiplied by the periodic rate to find the interest for that period.
Why does this matter to a business? Because the more often interest is added, the more total interest is paid.
Interest added in each period earns interest in the next, so the effective annual rate is higher than the stated annual rate when compounding happens more than once a year. Credit card agreements state the periodic rate on every statement, and the annual percentage rate shown is derived from it.
Anyone comparing financing offers should use the periodic rate and the number of periods to compute the cost, rather than relying on a rounded headline figure. The same arithmetic underlies loan amortisation schedules and bond coupon calculations.
A nuance is that the nominal annual rate (the periodic rate multiplied by the number of periods) is not the same as the effective annual rate. The effective rate allows for compounding and is the one that tells you the true yearly cost or return.
In practice
Real-world examples.
Example
A retailer's supplier offers credit and charges 24% a year on overdue invoices, applied monthly. The periodic rate is 2% per month, so an overdue $20,000 invoice adds $400 of interest in the first month. If the invoice stays unpaid, the second month's interest is charged on a larger balance.
Example
An investor buys a bond paying 6% a year in two instalments. The periodic rate is 3% per half year, so each coupon on a $10,000 bond is $300. The investor receives two such payments a year, giving $600 in total.
Example
A homeowner has a mortgage at 4.8% a year with monthly payments. The monthly periodic rate is 4.8% / 12 = 0.4%, which the lender applies to the outstanding balance each month. On a $300,000 balance, the first month's interest is $1,200.
Formula
Calculation
Periodic interest rate = annual rate / number of periods per year
Effective annual rate = (1 + periodic rate) ^ number of periods - 1
Suppose a business credit card charges an annual rate of 18% compounded monthly. The periodic rate is 18% / 12 = 1.5% per month. On an unpaid balance of $5,000, the first month's interest is 5,000 x 0.015 = $75. After 12 months of compounding, 1.015 raised to the power of 12 is about 1.1956, so the effective annual rate is about 19.56%, which is higher than the stated 18%.Case study
Seen in the real world.
Kestrel Print is an illustrative, fictional company that financed new equipment with a $60,000 loan at 12% a year, compounded monthly. The owner thought the cost was simply 12% of $60,000 per year.
The finance manager explained that the periodic rate was 1% per month, so interest was charged on a balance that changed every month. In the first month the interest was 60,000 x 0.01 = $600.
She also showed that with monthly compounding the effective annual rate is about 12.68%, not 12%. The owner used that figure to compare the loan with a competing offer quoted with annual compounding, and the illustrative lesson is that offers should be compared on an effective rate rather than on a headline rate. The owner chose the cheaper loan after seeing the effective rates side by side.
Watch out
Common mistakes.
- Using the annual rate on a monthly balance, which overstates the interest by a factor of twelve.
- Treating the stated annual rate as the true cost when interest is compounded more than once a year.
- Comparing two financing offers with different compounding frequencies without converting them to the same basis.
Questions
People also ask.
How do you convert an annual rate to a monthly rate?
Divide the annual rate by 12 for the nominal monthly rate, for example 9% becomes 0.75% per month. For a quarterly rate, divide by 4 instead.
What is the difference between nominal and effective annual rates?
The nominal rate is the periodic rate multiplied by the number of periods, while the effective rate includes the effect of compounding and is therefore higher when compounding is frequent.
Does the periodic rate change over time?
It stays the same if the annual rate is fixed, but variable rate loans reset it when the benchmark rate changes. In that case the lender must tell the borrower the new rate in advance.
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