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Effective Annual Rate Calculator TI BA II Plus

Effective Annual Rate Formula:

\[ EAR = (1 + \frac{r}{n})^n - 1 \]

%
per year

1. What is Effective Annual Rate (EAR)?

Definition: EAR is the actual interest rate that an investor earns or pays in a year after accounting for compounding.

Purpose: It allows comparison between investments with different compounding periods by showing their true annual yield.

2. How Does the EAR Calculator Work?

The calculator uses the formula:

\[ EAR = (1 + \frac{r}{n})^n - 1 \]

Where:

  • \( EAR \) — Effective Annual Rate (as decimal)
  • \( r \) — Nominal interest rate (as decimal)
  • \( n \) — Number of compounding periods per year

Explanation: The nominal rate is divided by compounding periods, compounded, then converted back to annual rate.

3. Importance of EAR Calculation

Details: EAR reveals the true cost of loans or true yield of investments, especially when comparing products with different compounding frequencies.

4. Using the Calculator

Tips: Enter the nominal interest rate (as percentage) and number of compounding periods per year (default 12 for monthly). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why is EAR higher than nominal rate?
A: Because of compounding - interest earns more interest when compounded more frequently.

Q2: What's the difference between APR and EAR?
A: APR doesn't account for compounding, while EAR does, making EAR the true rate.

Q3: How does continuous compounding work?
A: For continuous compounding, use the formula \( EAR = e^r - 1 \) where e ≈ 2.71828.

Q4: What's a typical compounding frequency?
A: Common frequencies: 1 (annual), 2 (semi-annual), 4 (quarterly), 12 (monthly), 365 (daily).

Q5: How do I calculate EAR on TI BA II Plus?
A: Use the ICONV worksheet: [2nd][ICONV], enter nominal rate [↓], set C/Y, [↓] to see EFF.

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