What rate of interest compounded quarterly will yield an effective interest rate of 6%? Round the answer to three decimal places.

To find the nominal interest rate \( r \) compounded quarterly that yields an effective interest rate of 6%, we can use the following formula:

\[
(1 + \frac{r}{n})^n = 1 + i_{\text{effective}}
\]

Where:
- \( r \) is the nominal interest rate (annual interest rate)
- \( n \) is the number of compounding periods per year (for quarterly compounding, \( n = 4 \))
- \( i_{\text{effective}} \) is the effective interest rate (6%, or 0.06 in decimal form)

Now, we can plug in the values:

\[
(1 + \frac{r}{4})^4 = 1.06
\]

We need to solve for \( r \). Let's calculate this step-by-step.

First, take the fourth root of both sides:

\[
1 + \frac{r}{4} = (1.06)^{1/4}
\]

Now, subtract 1 from both sides:

\[
\frac{r}{4} = (1.06)^{1/4} - 1
\]

Finally, multiply by 4 to solve for \( r \):

\[
r = 4 \left( (1.06)^{1/4} - 1 \right)
\]

Let me compute this.The nominal interest rate compounded quarterly that will yield an effective interest rate of 6% is approximately **5.9%**.

Would you like further clarification or details on this calculation?

Here are 5 related questions you might explore:
1. What is the formula for effective interest rate when compounding is monthly?
2. How does continuous compounding differ from quarterly compounding?
3. What nominal interest rate would yield a 7% effective interest rate with quarterly compounding?
4. How do different compounding periods affect the nominal interest rate?
5. Can you derive the effective interest rate from a given nominal interest rate?

**Tip:** The more frequent the compounding period, the closer the nominal and effective interest rates will be!

What rate of interest compounded quarterly will yield an effective interest rate of 6%? Round the answer to three decimal places.

Learn how to calculate the nominal interest rate compounded quarterly to yield an effective interest rate of 6%. This detailed guide includes key formulas, step-by-step solutions, and mathematical concepts for college-level students studying finance or mathematics.

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