You deposit $ 10 comma 000 in an account that pays 1.43 % interest compounded quarterly.
a. Find the future value after one year.
b. Use the future value formula for simple interest to determine the effective annual yield.
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Part 1
a. The future value is ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)

To solve this, we will use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $A$ is the future value.
- $P$ is the principal amount (initial deposit), which is \$10,000.
- $r$ is the annual interest rate (1.43%, or 0.0143).
- $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$).
- $t$ is the number of years (1 year in this case).

### Step 1: Plug the values into the formula

\[
A = 10{,}000 \left(1 + \frac{0.0143}{4}\right)^{4 \times 1}
\]

Now, let's calculate it step by step.The future value after one year is approximately **\$10,143.77**.

### Part (b): Effective Annual Yield (EAY)
The formula for effective annual yield (EAY) using compound interest is:

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

Now, let's calculate the effective annual yield using the given interest rate.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the process of calculating the effective annual yield (EAY) yourself:

### EAY Formula:
\[
\text{EAY} = \left(1 + \frac{r}{n}\right)^n - 1
\]

Where:
- $r = 0.0143$ (the annual interest rate),
- $n = 4$ (quarterly compounding).

### Plugging in the values:
\[
\text{EAY} = \left(1 + \frac{0.0143}{4}\right)^4 - 1
\]

After calculating this, multiply the result by 100 to express it as a percentage.

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Would you like more details, or do you have any questions? Here are some related questions:

1. How does changing the compounding frequency affect future value?
2. How do different interest rates impact the effective annual yield?
3. What is the difference between nominal and effective interest rates?
4. How is continuous compounding different from quarterly compounding?
5. What is the significance of the effective annual yield in investment decisions?

**Tip**: Compounding more frequently results in a higher effective annual yield!

You deposit $10,000 in an account that pays 1.43% interest compounded quarterly. a. Find the future value after one year. b. Use the future value formula for simple interest to determine the effective annual yield.

Calculate the future value of a $10,000 deposit with 1.43% interest compounded quarterly, and determine the effective annual yield. This finance problem covers compound interest and exponential growth. Ideal for students in Grades 10-12.

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