How to Calculate Apr from Monthly Rate

Monthly Rate to APR Converter

Enter the periodic rate found on your statement.

Nominal APR

0.00%

Simple Annualized Rate (Rate × 12)

Effective APR (EAR)

0.00%

With Compounding Included

Explanation: A monthly rate of % results in a nominal APR of %. If the interest compounds monthly, the actual cost (Effective APR) is %.

Please enter a valid numeric monthly rate.

function calculateAPR() { // Get input value var monthlyRateInput = document.getElementById('monthlyRateInput'); var resultContainer = document.getElementById('resultContainer'); var errorMessage = document.getElementById('error-message'); var monthlyRateVal = parseFloat(monthlyRateInput.value); // Validation if (isNaN(monthlyRateVal) || monthlyRateVal 0.01) var rateDecimal = monthlyRateVal / 100; var effectiveAPRDecimal = Math.pow((1 + rateDecimal), 12) – 1; var effectiveAPR = effectiveAPRDecimal * 100; // Display Results document.getElementById('nominalAPRResult').innerHTML = nominalAPR.toFixed(2) + '%'; document.getElementById('effectiveAPRResult').innerHTML = effectiveAPR.toFixed(2) + '%'; // Update explanation text document.getElementById('displayMonthlyInput').innerHTML = monthlyRateVal.toFixed(2); document.getElementById('displayNominalText').innerHTML = nominalAPR.toFixed(2); document.getElementById('displayEffectiveText').innerHTML = effectiveAPR.toFixed(2); // Show results resultContainer.style.display = 'block'; }

Understanding the true cost of borrowing requires looking beyond the monthly interest rate shown on your credit card statement or loan agreement. While the monthly rate dictates your immediate interest charges, the Annual Percentage Rate (APR) provides a standardized annual figure for comparison. This guide explains how to convert a monthly periodic rate into an annual figure and the difference between nominal and effective rates.

The Difference Between Monthly Rate and APR

In finance, interest rates are often quoted in different time frames. The Monthly Periodic Rate is the percentage of interest charged on the outstanding principal balance at the end of each month. The APR is the annualized version of this rate.

There are two primary ways to express this annualized rate:

1. Nominal APR: This is the simple interest rate calculated without considering compounding. It is the standard figure used in most consumer lending disclosures (like the Truth in Lending Act in the US).
2. Effective Annual Rate (EAR) or APY: This figure accounts for the effect of compounding interest, where interest is charged on top of previously accumulated interest.

Formula 1: Calculating Nominal APR

The calculation for the Nominal APR is straightforward multiplication. Since there are 12 months in a year, you simply multiply the monthly rate by 12.

APR = Monthly Rate × 12

Example: If your credit card has a monthly periodic rate of 1.5%:

• Calculation: 1.5 × 12 = 18.00%
• Nominal APR: 18.00%

Formula 2: Calculating Effective Annual Rate (Compound Interest)

While the Nominal APR is useful for quick checks, it slightly underestimates the true cost if you carry a balance for a full year, because you pay interest on your interest. To find the "Effective" APR, the formula is exponential:

EAR = [(1 + r)¹² – 1] × 100

Where 'r' is the monthly rate expressed as a decimal (e.g., 1.5% becomes 0.015).

Using the same 1.5% example:

• Convert to decimal: 1.5 ÷ 100 = 0.015
• Add 1: 1.015
• Raise to power of 12: 1.015¹² ≈ 1.1956
• Subtract 1: 0.1956
• Convert to percentage: 19.56%

As you can see, the effect of compounding makes the effective rate (19.56%) higher than the nominal APR (18.00%).

Why Credit Cards Use Daily or Monthly Rates

Credit card issuers calculate finance charges based on your average daily balance or ending monthly balance. Because billing cycles are monthly, the math is performed using the periodic rate. However, to comply with federal regulations, they must disclose the APR prominently. Knowing how to convert between the two helps you verify that the interest being charged matches the terms you agreed to.

Quick Reference Conversion Table

Monthly Rate	Nominal APR	Effective APR
0.50%	6.00%	6.17%
1.00%	12.00%	12.68%
1.50%	18.00%	19.56%
2.00%	24.00%	26.82%
2.50%	30.00%	34.49%