Troy deposits $6000
. Determine the APY if there is an APR of 7.5%
 compounded quarterly. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.
 

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.

Troy deposits $6000. Determine the APY if there is an APR of 7.5% compounded quarterly. Express your answer as a percentage rounded to the nearest hundredth of a percent, if necessary.

Learn how to calculate the Annual Percentage Yield (APY) from a 7.5% Annual Percentage Rate (APR) compounded quarterly. This problem demonstrates the compound interest formula and its application, with step-by-step calculations. Suitable for students in Grades 9-12.

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