What is the APY for an account that has an annual interest rate of 4.9% and is compounded daily (n=365)? In the image. Round your answer to the hundredth of a percent.
What is the APY for an account that has an annual interest rate of 4.9% and is compounded daily (n=365)? In the image. Round your answer to the hundredth of a percent.
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 68SE: An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000...
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What is the APY for an account that has an annual interest rate of 4.9% and is compounded daily (n=365)? In the image. Round your answer to the hundredth of a percent.
![### Understanding Annual Percentage Yield (APY)
The formula for calculating Annual Percentage Yield (APY) is:
\[ APY = \left(1 + \frac{r}{n}\right)^n - 1 \]
#### Explanation of Variables:
- **APY:** Annual Percentage Yield, which represents the actual rate of return earned on an investment, taking into account the effect of compounding interest.
- **r:** Nominal interest rate or the annual interest rate.
- **n:** Number of compounding periods per year.
#### Detailed Breakdown:
1. **\(\frac{r}{n}\):** This component divides the nominal annual interest rate \(r\) by the number of compounding periods per year \(n\), giving the interest rate for each compounding period.
2. **\(\left(1 + \frac{r}{n}\right)\):** Adding 1 to the periodic interest rate calculates the growth factor for one compounding period.
3. **\(\left(1 + \frac{r}{n}\right)^n\):** Raising the growth factor to the power of \(n\) (the number of compounding periods) calculates the total growth factor for the whole year.
4. **\(- 1\):** Subtracting 1 from the total growth factor removes the principal amount, isolating the APY.
#### Graphical Interpretation:
If a graph were included with the formula, it might depict the effect of different compounding frequencies on the APY. For example:
- **X-Axis:** Number of compounding periods per year (e.g., annually, semi-annually, quarterly, monthly, daily).
- **Y-Axis:** Corresponding APY values.
The graph would typically show that as the number of compounding periods increases, the APY also increases, demonstrating the power of compounding interest more frequently.
### Application:
Understanding APY is crucial for investors when comparing different financial products such as savings accounts, certificates of deposit (CDs), and other interest-bearing accounts. Higher APY indicates a better return on investment due to more frequent compounding of interest.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27b4bc7f-06c3-4245-81d4-6188c9348506%2F2e5c4ed5-01ed-4a24-b93b-25f7f8862133%2F670sjs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Annual Percentage Yield (APY)
The formula for calculating Annual Percentage Yield (APY) is:
\[ APY = \left(1 + \frac{r}{n}\right)^n - 1 \]
#### Explanation of Variables:
- **APY:** Annual Percentage Yield, which represents the actual rate of return earned on an investment, taking into account the effect of compounding interest.
- **r:** Nominal interest rate or the annual interest rate.
- **n:** Number of compounding periods per year.
#### Detailed Breakdown:
1. **\(\frac{r}{n}\):** This component divides the nominal annual interest rate \(r\) by the number of compounding periods per year \(n\), giving the interest rate for each compounding period.
2. **\(\left(1 + \frac{r}{n}\right)\):** Adding 1 to the periodic interest rate calculates the growth factor for one compounding period.
3. **\(\left(1 + \frac{r}{n}\right)^n\):** Raising the growth factor to the power of \(n\) (the number of compounding periods) calculates the total growth factor for the whole year.
4. **\(- 1\):** Subtracting 1 from the total growth factor removes the principal amount, isolating the APY.
#### Graphical Interpretation:
If a graph were included with the formula, it might depict the effect of different compounding frequencies on the APY. For example:
- **X-Axis:** Number of compounding periods per year (e.g., annually, semi-annually, quarterly, monthly, daily).
- **Y-Axis:** Corresponding APY values.
The graph would typically show that as the number of compounding periods increases, the APY also increases, demonstrating the power of compounding interest more frequently.
### Application:
Understanding APY is crucial for investors when comparing different financial products such as savings accounts, certificates of deposit (CDs), and other interest-bearing accounts. Higher APY indicates a better return on investment due to more frequent compounding of interest.
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