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Effective Interest Rate Calculation:

The effective interest rate is calculated numerically as there is no closed-form formula. It solves for the rate that equates the present value of cash inflows and outflows.

Effective Annual Rate:

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1. What is Effective Interest Rate?

The effective interest rate (EIR) is the actual interest rate that an investor earns or a borrower pays after accounting for compounding over a given period. It differs from the nominal rate which doesn't consider compounding frequency.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ EIR = \left(1 + \frac{r}{n}\right)^n - 1 \]

Where:

\( r \) — Nominal interest rate (as decimal)
\( n \) — Number of compounding periods per year

Explanation: The formula accounts for the effect of compounding, showing the true cost of borrowing or true return on investment.

3. Importance of Effective Rate

Details: Comparing financial products requires EIR as nominal rates can be misleading. It's crucial for loans, investments, and financial planning.

4. Using the Calculator

Tips: Enter the nominal annual interest rate and the number of compounding periods per year (e.g., 12 for monthly, 4 for quarterly).

5. Frequently Asked Questions (FAQ)

Q1: Why is effective rate higher than nominal rate?
A: Because it accounts for compounding - interest earned on previously accumulated interest.

Q2: How does compounding frequency affect the rate?
A: More frequent compounding results in higher effective rates for the same nominal rate.

Q3: What's the difference between APR and EIR?
A: APR is typically the nominal rate, while EIR includes compounding effects.

Q4: When is EIR most important?
A: For comparing loans/investments with different compounding periods or payment structures.

Q5: Can EIR be calculated for continuous compounding?
A: Yes, using the formula \( e^r - 1 \) where r is the nominal rate and e is Euler's number.