How interest rate conversion works
Interest rates are quoted for a specific time period. A monthly rate, a quarterly rate, and an annual rate can all describe the same underlying cost of money, but only if converted correctly before comparison. A credit card charging 1.5% per month and a personal loan quoting 18% per year are in fact identical. Converting between periods requires choosing the right method for the context.
Two conversion methods exist. Simple (proportional) conversion multiplies or divides the rate directly by the number of periods per year. This is fast and is the method used in most consumer loan APR disclosures. Compound (equivalent) conversion accounts for the fact that interest accrues between periods, and each period's interest itself earns interest in subsequent periods. This gives the Effective Annual Rate (EAR) and is the correct method when comparing products that compound frequently, such as savings accounts or mortgages.
The conversion formulas
Simple (proportional) conversion:
Annual rate = periodic rate × n
Periodic rate = annual rate ÷ n
Compound (equivalent) conversion:
Annual EAR = (1 + periodic rate)^n − 1
Periodic rate = (1 + annual EAR)^(1/n) − 1
Converting between two non-annual periods (always route via annual):
Step 1: input period → annual (simple or compound)
Step 2: annual → target period (simple or compound)
n = number of periods per year: 365 (daily), 52 (weekly), 26 (bi-weekly), 12 (monthly), 4 (quarterly), 2 (semi-annual), 1 (annual). Routing all conversions through the annual rate avoids accumulated rounding errors when jumping between non-adjacent periods such as daily to quarterly.
Quick reference: common conversions
| Input rate | From period | Simple annual | Compound annual (EAR) | Simple monthly | Compound monthly |
|---|
| 0.500% | Monthly | 6.000% | 6.168% | 0.500% | 0.500% |
| 1.000% | Monthly | 12.000% | 12.683% | 1.000% | 1.000% |
| 1.500% | Monthly | 18.000% | 19.562% | 1.500% | 1.500% |
| 3.000% | Quarterly | 12.000% | 12.551% | 1.000% | 0.990% |
| 6.000% | Annual | 6.000% | 6.000% | 0.500% | 0.487% |
| 12.000% | Annual | 12.000% | 12.000% | 1.000% | 0.949% |
| 0.016% | Daily | 5.921% | 6.083% | 0.493% | 0.487% |
When simple and compound give the same answer
Simple and compound conversion give identical results in exactly one case: when converting an annual rate to an annual rate (n = 1). In all other cases they diverge. The divergence is smallest at low rates and long periods (0.5% monthly to annual: 0.168 pp gap), and largest at high rates (3% monthly to annual: 6.576 pp gap). The gap always runs in the same direction: compound annual is always higher than simple annual when scaling up, and compound periodic is always lower than simple periodic when scaling down from annual.
Which method to use in practice
Use simple conversion when you are working with nominal rates for legal APR disclosures, comparing loans where the lender has specified a simple nominal rate, or performing quick mental arithmetic. Use compound conversion whenever you want the true economic cost or yield: comparing a savings AER to a loan APR, evaluating total interest cost on a compound-interest loan, or computing the equivalent periodic rate for an amortisation schedule. When in doubt, convert both ways and note the gap. If the two methods give results that are meaningfully different, the compound figure is the more accurate economic measure.
Worked examples
Example 1: Credit card monthly rate to annual
A credit card charges 1.5% per month. Simple annual APR: 1.5% × 12 = 18.00%. Compound annual EAR: (1.015)^12 − 1 = 19.562%. The 1.562 percentage point gap means that on a $5,000 balance carried for a full year, you would pay $900 in simple interest but $978.10 under compound calculation. The compound figure is the true cost.
Example 2: Annual rate to monthly (mortgage)
A mortgage is quoted at 6% APR. Simple monthly rate: 6% ÷ 12 = 0.500%. This is the rate used in the standard mortgage payment formula. Compound equivalent monthly rate: (1.06)^(1/12) − 1 = 0.4868%. The difference is small but on a $300,000 mortgage it affects the payment calculation by several dollars per month and hundreds of dollars over the life of the loan.
Example 3: Quarterly rate to monthly (compound)
A bond pays 3% per quarter. Simple annual: 3% × 4 = 12.00%. Compound annual EAR: (1.03)^4 − 1 = 12.551%. Compound monthly equivalent: (1.12551)^(1/12) − 1 = 0.990%. This is the correct rate to use if you need to compare this bond against a monthly-paying savings account. The simple monthly equivalent would be 1.000%, overstating the true monthly yield by 0.010 pp.
Example 4: Daily rate to annual (credit card US style)
US credit cards often quote a Daily Periodic Rate (DPR). A DPR of 0.04932% (18% APR ÷ 365) converts to: Simple annual: 0.04932% × 365 = 18.000%. Compound annual EAR: (1.0004932)^365 − 1 = 19.716%. The EAR is 1.716 percentage points above the headline APR. On a $1,000 balance this means $197.16 in compound interest versus $180 simple, a $17.16 difference in one year that grows larger at higher balances.
| Scenario | Input rate / period | Simple annual | EAR | Gap |
|---|
| Credit card (monthly) | 1.5% monthly | 18.000% | 19.562% | 1.562 pp |
| Mortgage (annual APR) | 6.0% annual | 6.000% | 6.000% | 0.000 pp |
| Bond (quarterly) | 3.0% quarterly | 12.000% | 12.551% | 0.551 pp |
| Savings (daily) | 0.016% daily | 5.921% | 6.083% | 0.162 pp |
| Payday loan (monthly) | 3.0% monthly | 36.000% | 42.576% | 6.576 pp |
Frequently Asked Questions
When should I use simple versus compound conversion?+
Use simple (proportional) conversion when working with nominal APR rates as disclosed by lenders, when performing quick mental calculations, or when the loan product explicitly uses simple interest. Simple conversion is the standard for consumer credit APR disclosures in the EU and UK because it is transparent and easy to verify. Use compound (equivalent) conversion when you want to understand the true economic cost or yield, compare products with different compounding frequencies, or calculate the exact periodic rate for use in an amortisation schedule. As a general rule: for regulatory disclosure, simple; for economic comparison, compound.
Why is the compound annual rate always higher than the simple rate when converting up?+
When converting a periodic rate (say, monthly) to an annual rate, compound conversion accounts for the fact that interest earned in each period is added to the balance and itself earns interest in subsequent periods. A 1% monthly rate means 1% is earned on the original balance in January, but February's 1% is earned on a balance that is already 1% higher. After 12 months of this, the total growth is 12.683%, not 12%. Conversely, when scaling down from annual to monthly, the compound monthly rate must be slightly lower than the simple rate because the compounding effect over 12 periods needs to produce only the target annual rate, requiring a smaller periodic contribution than a direct division would give.
Why should I route conversions via the annual rate?+
When converting between two non-annual periods directly (for example, daily to quarterly), there is a risk of accumulated rounding error if you try to compute the conversion in a single step without going through the annual rate. The recommended method is always to first convert the input periodic rate to an annual rate, then convert that annual rate to the target period. This two-step approach uses the same well-tested formulas in both steps and avoids the precision issues that can arise from raising small numbers to large powers or computing fractional exponents of non-annual rates. The calculator performs this routing automatically.
How do I convert a daily rate to a monthly rate?+
Simple method: monthly rate = daily rate × (365 ÷ 12) = daily rate × 30.4375. For a daily rate of 0.02%, this gives 0.02% × 30.4375 = 0.609% monthly. Compound method: monthly rate = (1 + daily rate)^(365/12) − 1. For a daily rate of 0.02%, compound monthly = (1.0002)^(30.4375) − 1 = 0.611%. This calculator uses 365 days per year and 365/12 = 30.4375 days per month consistently across all conversions. Using calendar days (28 to 31 per month) would give slightly different results, but 30.4375 is the standard assumption in financial calculations.
What is a bi-weekly rate and when does it appear?+
A bi-weekly rate applies to a two-week period. There are exactly 26 bi-weekly periods per year (52 weeks ÷ 2). Bi-weekly rates appear in some loan repayment schemes where payments are linked to payroll cycles, in certain mortgage products where bi-weekly payments accelerate payoff by producing one extra full payment per year, and occasionally in hire-purchase or lease agreements. A bi-weekly rate of 0.25% simple gives 0.25% × 26 = 6.5% annual. Compound: (1.0025)^26 − 1 = 6.777% EAR. The bi-weekly equivalent of a 6% annual rate is 6% ÷ 26 = 0.2308% simple, or (1.06)^(1/26) − 1 = 0.2237% compound.
How does this calculator differ from the APR vs Nominal Rate calculator?+
The APR vs Nominal Rate calculator focuses on converting between a nominal rate and its Effective Annual Rate (EAR) for a given compounding frequency. It also supports the reverse direction (EAR to nominal) and continuous compounding. This Interest Rate Converter focuses on converting a rate quoted for one specific period (such as monthly) into equivalent rates for every other period simultaneously — daily, weekly, bi-weekly, monthly, quarterly, semi-annual, and annual — showing both simple and compound values in a full comparison table. Use the APR vs Nominal Rate calculator when you want to understand the EAR impact of compounding. Use this converter when you need to translate a rate from one quoted period into all other periods for a complete picture.