The effective interest rate on your credit card is 38 percent. What is the equivalent nominal interest rate if interest compounds​ daily? (EFF)

To find the equivalent nominal interest rate given an effective interest rate (EFF) of 38% and daily compounding, we can use the following formula that links the nominal interest rate (\( r_{nom} \)) and the effective interest rate (\( r_{eff} \)):

\[
r_{eff} = \left( 1 + \frac{r_{nom}}{n} \right)^n - 1
\]

Where:
- \( r_{eff} \) is the effective interest rate (38% or 0.38).
- \( r_{nom} \) is the nominal interest rate (what we are solving for).
- \( n \) is the number of compounding periods per year (for daily compounding, \( n = 365 \)).

We can now rearrange this formula to solve for the nominal interest rate (\( r_{nom} \)):

\[
1 + \frac{r_{nom}}{n} = \left( 1 + r_{eff} \right)^{1/n}
\]

Solving for \( r_{nom} \):

\[
r_{nom} = n \times \left[ \left( 1 + r_{eff} \right)^{1/n} - 1 \right]
\]

Let me calculate this for you.The equivalent nominal interest rate, with daily compounding, is approximately **32.22%**.

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The effective interest rate on your credit card is 38 percent. What is the equivalent nominal interest rate if interest compounds daily? (EFF)

Discover how to calculate the nominal interest rate from a 38% effective interest rate when interest compounds daily. This problem explores key concepts like interest rates, compounding, and exponential functions, making it ideal for high school students (Grades 11-12).

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