You deposit $ 12 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 ​$
  
12172.52.
​(Round to the nearest cent as​ needed.)
Part 2
b. The effective annual yield is 
  
enter your response here​%.
​(Round to the nearest hundredth as​ needed.)

Let's go through the steps to find the future value and the effective annual yield for your problem.

### Part 1: Future Value after One Year

The formula for future value with compound interest is:

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

Where:
- $ A $ is the future value
- $ P $ is the principal amount ($12,000)
- $ r $ is the annual interest rate (1.43% = 0.0143)
- $ n $ is the number of times the interest is compounded per year (quarterly = 4)
- $ t $ is the number of years (1 year)

Now plug the values into the formula:

\[
A = 12,000 \left(1 + \frac{0.0143}{4}\right)^{4 \times 1}
\]

Simplify:

\[
A = 12,000 \left(1 + 0.003575\right)^{4}
\]
\[
A = 12,000 \times (1.003575)^4
\]
\[
A \approx 12,000 \times 1.014376
\]
\[
A \approx 12,172.52
\]

So, the future value after one year is **$12,172.52**.

### Part 2: Effective Annual Yield (EAY)

The effective annual yield is calculated using the formula:

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

Where:
- $ r $ is the nominal annual interest rate (1.43% = 0.0143)
- $ n $ is the number of compounding periods per year (quarterly = 4)

Substitute the values:

\[
\text{EAY} = \left(1 + \frac{0.0143}{4}\right)^4 - 1
\]
\[
\text{EAY} = \left(1 + 0.003575\right)^4 - 1
\]
\[
\text{EAY} \approx 1.014376 - 1
\]
\[
\text{EAY} \approx 0.014376
\]

Convert this to a percentage:

\[
\text{EAY} \approx 1.44\%
\]

So, the **effective annual yield is 1.44%**.

---

Would you like more details or have any questions? Here are some related questions for practice:

1. How would the future value change if the interest rate was 2%?
2. What would be the future value after 2 years instead of 1 year?
3. How is the future value affected if the interest is compounded monthly instead of quarterly?
4. What happens to the effective annual yield if interest is compounded semi-annually?
5. How would you calculate the future value if the principal was $15,000 instead of $12,000?

**Tip:** Always make sure to check whether interest is compounded annually, semi-annually, quarterly, or monthly—it makes a significant difference in the calculation!

You deposit $12,000 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.

Learn how to calculate the future value and effective annual yield for a $12,000 deposit at 1.43% interest compounded quarterly. This example demonstrates the use of compound interest formulas to determine future value and yield, perfect for Grades 10-12.

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