Apy Verification 92E6E5
1. **State the problem:** We are given an interest rate of 8.3% compounded quarterly and an advertised APY (Annual Percentage Yield) of 8.56%. We need to verify if this APY is accurate.
2. **Formula for APY:** The APY is calculated using the formula:
$$\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1$$
where $r$ is the nominal annual interest rate (as a decimal), and $n$ is the number of compounding periods per year.
3. **Given values:**
- Nominal interest rate $r = 8.3\% = 0.083$
- Compounding periods per year $n = 4$ (quarterly)
4. **Calculate APY:**
$$\text{APY} = \left(1 + \frac{0.083}{4}\right)^4 - 1 = \left(1 + 0.02075\right)^4 - 1$$
Calculate inside the parentheses:
$$1.02075^4 - 1$$
Calculate $1.02075^4$:
$$1.02075^4 = 1.0856$$ (rounded to 4 decimal places)
So,
$$\text{APY} = 1.0856 - 1 = 0.0856 = 8.56\%$$
5. **Interpretation:** The calculated APY is 8.56%, which matches the advertised APY.
6. **Conclusion:** The advertisement is accurate.
**Final answer:** Yes. The information in the advertisement is accurate.