To find the equivalent nominal interest rate (also known as the Annual Percentage Rate, or APR) when the effective interest rate (EFF) is given, and the interest compounds daily, we can use the following formula:

$EFF = \left(1 + \frac{i}{n}\right)^n - 1$

Where:

• $EFF$ is the effective annual interest rate (32% or 0.32),
• $i$ is the nominal interest rate (APR),
• $n$ is the number of compounding periods per year (365 for daily compounding).

We need to solve for $i$. The formula can be rearranged as:

$1 + EFF = \left(1 + \frac{i}{n}\right)^n$

Taking the $n$-th root on both sides:

$1 + \frac{i}{n} = \left(1 + EFF\right)^{\frac{1}{n}}$

Solving for $i$:

$i = n \left[\left(1 + EFF\right)^{\frac{1}{n}} - 1\right]$

Let me calculate the nominal interest rate (APR).The equivalent nominal interest rate (APR) when the effective interest rate is 32% with daily compounding is approximately 27.77%.

Would you like more details or have any questions about this calculation?

Here are 5 related questions for deeper understanding:

1. How does the effective interest rate differ from the nominal interest rate?
2. What happens to the nominal rate if interest compounds monthly instead of daily?
3. How can you calculate the effective interest rate if you know the nominal rate?
4. Why does daily compounding reduce the nominal interest rate compared to the effective rate?
5. What is the impact of increasing the number of compounding periods on the effective interest rate?

Tip: The more frequently interest is compounded, the closer the nominal and effective interest rates become.