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Equivalent Rate (AER) Calculator

Convert a nominal rate from one compounding frequency to another and compute the Effective Annual Rate (AER).

Equivalent Rate (AER) Calculator

Interest rates are often expressed with different compounding frequencies, which can make comparing investments or loans confusing. The Equivalent Rate (AER) Calculator helps solve this problem by converting a nominal interest rate from one compounding frequency to another. It also computes the Effective Annual Rate (EAR or AER), ensuring you know the true return or cost of borrowing.

Whether you’re comparing savings accounts, fixed deposits, or loan offers, this calculator makes it simple to find equivalent rates and make smarter financial decisions.

🔎 What is Equivalent Rate (AER)?

The Equivalent Rate, also known as the Annual Equivalent Rate (AER), allows you to compare interest rates with different compounding frequencies.

👉 Formula for Equivalent Rate:

The equivalent nominal rate at a new frequency is calculated using the relationship between the original nominal rate, original compounding frequency, and the new compounding frequency.
The AER is then derived from:

AER = (1 + (Nominal Rate ÷ Original Frequency)) ^ Original Frequency – 1

This ensures that regardless of whether interest is compounded monthly, quarterly, or daily, you can calculate and compare the true annual return or cost.

📚 Step-by-Step Examples of Equivalent Rate (AER) Calculations

Example 1

Nominal Interest Rate (i): 8%
Original Compounding Frequency (n₁): 4 (Quarterly)
New Compounding Frequency (n₂): 12 (Monthly)

Step 1 – Convert Nominal Rate to Effective Annual Rate (EAR):

EAR = (1 + 0.08/4) ^ 4 – 1 = (1.02) ^ 4 – 1 = 0.082432 = 8.243216%

Step 2 – Convert EAR to Equivalent Nominal Rate at New Frequency:

Equivalent Nominal Rate = 12 × [(1.082432)^(1/12) – 1] = 7.947251%

✅ Equivalent Nominal Rate (Monthly) = 7.95%
✅ Effective Annual Rate (AER) = 8.24%

Example 2

Nominal Interest Rate (i): 10%
Original Compounding Frequency (n₁): 2 (Semi-Annually)
New Compounding Frequency (n₂): 52 (Weekly)

Step 1 – Convert Nominal Rate to Effective Annual Rate (EAR):

EAR = (1 + 0.10/2) ^ 2 – 1 = 1.1025 – 1 = 0.1025 = 10.25%

Step 2 – Convert EAR to Equivalent Nominal Rate at New Frequency:

Equivalent Nominal Rate = 52 × [(1.1025)^(1/52) – 1] = 9.77%

✅ Equivalent Nominal Rate (Weekly) = 9.77%
✅ Effective Annual Rate (AER) = 10.25%

Example 3 – Annual to Daily Conversion

Nominal Interest Rate (i): 12%
Original Compounding Frequency (n₁): 1 (Annually)
New Compounding Frequency (n₂): 365 (Daily)

Step 1 – Convert Nominal Rate to Effective Annual Rate (EAR):

EAR = (1 + 0.12/1) ^ 1 – 1 = 12%

Step 2 – Convert EAR to Equivalent Nominal Rate at New Frequency:

Equivalent Nominal Rate = 365 × [(1.12)^(1/365) – 1] = 11.33%

Step 3 – Confirm AER (Daily Compounding):

(1 + 0.1191 ÷ 365) ^ 365 – 1 = 12%

✅ Equivalent Nominal Rate (Daily) = 11.33%
✅ Effective Annual Rate (AER) = 12%

✨ Features of Our Equivalent Rate (AER) Calculator

✅ Instant and accurate conversions between compounding frequencies
✅ Calculates both Equivalent Nominal Rate and AER
✅ User-friendly design for professionals and beginners alike
✅ Works seamlessly on desktop, tablet, and mobile devices
✅ Completely free to use – no registration required
✅ Perfect for investors, borrowers, students, and financial analysts

👩‍💼 Who Should Use This Calculator?

Investors – To compare returns across different savings accounts, bonds, or deposits.
Borrowers – To evaluate loans with varying compounding structures.
Financial Analysts – To standardize rates for comparison in reports.
Students & Educators – To understand the impact of compounding frequency on rates.
Business Owners – To assess financing and investment options accurately.

💡 Why Equivalent Rate Matters

Financial products often advertise nominal rates without specifying compounding details, which can be misleading. A loan with monthly compounding at 12% is not the same as one with annual compounding at 12%, because the effective cost differs.
Using the Equivalent Rate (AER) ensures you’re comparing apples to apples, eliminating confusion caused by different compounding frequencies.

🌍 Practical Applications of Equivalent Rate Calculations

Banking & Savings – Compare savings accounts with different compounding schedules.
Fixed Deposits & Bonds – Assess real returns across investment products.
Loans & Mortgages – Identify the true cost of borrowing across lenders.
Financial Research – Standardize rates for data analysis and valuation models.
Education – Demonstrate how compounding frequency affects interest rates.

✅ The Equivalent Rate (AER) Calculator is an essential tool for anyone making borrowing or investment decisions. Whether you’re an investor, student, borrower, or analyst, this tool ensures clarity and accuracy when comparing financial products with different compounding schedules.

👉 Try the Equivalent Rate (AER) Calculator today on Hive Calculator and simplify your interest rate comparisons with confidence!