Many rates are not quoted per year. Credit cards publish a monthly or daily periodic rate, short-term lenders charge a percentage per month, savings products credit interest each quarter, and investment returns are often reported per quarter or per month. When the rate is already “per period,” the cleanest way to compound it is the periodic form of the formula. This calculator does exactly that and translates the result into annual terms.
How to use the periodic compound interest calculator
- Choose what to solve for: future value, principal, rate per period or number of periods.
- Enter the known values: principal, rate per period, number of periods and/or future value.
- Choose what each period represents — day, week, month, quarter, half-year or year — so the calculator can express the rate annually.
- Read the result, the nominal and effective annual rates, and the period-by-period table and chart.
Periodic compound interest formulas
Rearranged:
With m periods in a year:
Worked example
You lend $5,000 at 1.5% per month, compounded monthly, for 18 months.
(1 + 0.015)18 = 1.30734064
A = 5,000 × 1.30734064 = $6,536.70; interest = $1,536.70
Nominal annual rate: 1.5% × 12 = 18%. Effective annual rate: 1.01512 − 1 = 19.56%
Working backward: if you want $6,500 back after 18 months, the monthly rate is (6,500 ÷ 5,000)1/18 − 1 = 1.4683%. At 1.5% a month, $5,000 reaches $6,500 after 17.62 months — in practice at the 18th monthly credit.
Periodic rates in everyday finance
| Where you see it | Typical quote | Annual equivalent |
|---|---|---|
| Credit card daily periodic rate | 0.0627% per day | ≈ 22.9% APR; about 25.7% effective |
| Short-term loan | 2% per month | 24% nominal; 26.82% effective |
| Savings credited quarterly | 1% per quarter | 4% nominal; 4.06% effective |
| Investment return | 0.5% per month | 6% nominal; 6.17% effective |
The nominal figure (rate × periods) is how APRs are disclosed in the US; the effective figure shows what the money actually grows by with compounding.
Tips for working with periodic rates
Keep the period consistent
The rate and the number of periods must use the same period. A monthly rate with time in years — or the reverse — is the most common mistake.
Know which annual rate you need
Comparing a loan quote with an APR? Use the nominal rate. Comparing savings returns or the true cost of borrowing? Use the effective annual rate. The effective annual rate calculator and the periodic interest rate calculator cover the conversions in both directions.
Adding deposits
This calculator compounds a single amount. If you add money every period, use the compound interest calculator, which handles regular contributions.
Results are estimates. Lenders and banks may count days, round interest or credit it on schedules that differ slightly from these assumptions.
Frequently asked questions
What is periodic compound interest?
It is compound interest expressed per period rather than per year. Instead of an annual rate and a compounding frequency, you have a rate i applied each period and a number of periods n, and the balance grows as A = P(1 + i)^n.
How do I convert a monthly rate to an annual rate?
Multiply by 12 to get the nominal annual rate, or compute (1 + i)^12 − 1 for the effective annual rate. A rate of 1.5% a month is 18% nominal but 19.56% effective, because each month's interest is compounded.
How do I find the rate per period from a start and end value?
Use i = (A ÷ P)^(1/n) − 1. If $5,000 grows to $6,500 in 18 months, the monthly rate is 1.3^(1/18) − 1 = 1.4683%.
Why is the number of periods not a whole number?
When you solve for n, the formula returns the exact time the balance reaches the target, which usually falls part-way through a period. In practice interest is credited at period ends, so the target is reached at the next whole period.