To determine the Annual Percentage Yield (APY) from the given Annual Percentage Rate (APR) compounded quarterly, we can use the formula for APY:

$APY = \left(1 + \frac{r}{n}\right)^n - 1$

Where:

• $r$ is the APR (in decimal form),
• $n$ is the number of compounding periods per year.

Given:

• APR = 7.5% = 0.075,
• Compounded quarterly, so $n = 4$.

Substituting the values into the formula:

$APY = \left(1 + \frac{0.075}{4}\right)^4 - 1$

Now we calculate this.The Annual Percentage Yield (APY) is approximately 7.71% when the APR is 7.5% compounded quarterly.

Do you want more details on how this was calculated or have any other questions?

Here are some related questions for further exploration:

1. How does the APY change if compounding is done monthly instead of quarterly?
2. What would be the APY for an APR of 6% compounded annually?
3. How does the APY compare for continuous compounding with the same APR?
4. How would the deposit grow after 5 years with this APY?
5. What is the difference between APR and APY in general?

Tip: APY is always higher than APR when compounding occurs more than once per year due to the effect of compound interest.