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!