Ms. Santoro is opening a one-year CD for $16,000. The interest is compounded daily. She is told by the bank representative that the annual percentage rate (APR) is 1.8%. What is the annual percentage yield (APY) for this account?

To calculate the **annual percentage yield (APY)** for an account with **daily compounding interest**, we can use the following formula:

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

Where:
- $ r $ is the annual interest rate (APR) in decimal form,
- $ n $ is the number of times the interest is compounded per year.

In this case:
- $ r = 1.8\% = 0.018 $,
- $ n = 365 $ (since the interest is compounded daily).

Let's calculate the APY:

\[
APY = \left(1 + \frac{0.018}{365}\right)^{365} - 1
\]

I'll calculate that now.The **annual percentage yield (APY)** for Ms. Santoro's account is approximately **1.82%**.

Would you like further details or have any other questions?

Here are some related questions for further exploration:
1. How does the frequency of compounding affect the APY?
2. What would the APY be if the interest were compounded monthly instead of daily?
3. How much total interest would Ms. Santoro earn after one year?
4. What happens if the APR changes over time?
5. How do different banks calculate APY for different types of accounts?

**Tip**: A higher compounding frequency (e.g., daily) will slightly increase the APY compared to a lower frequency (e.g., monthly).

Discover how to calculate the annual percentage yield (APY) for a one-year $16,000 CD with daily compounding at an APR of 1.8%. This problem covers key financial concepts such as interest rates and compounding, and demonstrates how the APY formula is applied. Ideal for high school students or anyone learning personal finance.

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