Calculate the amount of interest earned (in dollars) in 7 years on $12,000 deposited in an account paying 10% annual interest, compounded quarterly. (Round your answer to the nearest cent.)

To calculate the amount of interest earned, we can use the **compound interest formula**:

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

Where:
- $A$ is the future value of the investment/loan, including interest
- $P$ is the principal amount (initial deposit), which is \$12,000
- $r$ is the annual interest rate (as a decimal), which is 10% or 0.10
- $n$ is the number of times the interest is compounded per year, which is quarterly, so $n = 4$
- $t$ is the number of years, which is 7 years

We'll solve for $A$, the future value, and then subtract the initial deposit ($P$) to find the interest earned.

\[
A = 12000 \left(1 + \frac{0.10}{4}\right)^{4 \times 7}
\]

Now let’s calculate this.The future value of the investment after 7 years is approximately \$23,957.94. The interest earned is about **\$11,957.94**.

Would you like more details or have any questions? Here are 5 related questions to expand your understanding:

1. What if the interest rate were 8% instead of 10%?
2. How would the interest change if it were compounded monthly instead of quarterly?
3. What is the formula for simple interest, and how does it compare with compound interest?
4. How would the interest differ if the time period were reduced to 5 years?
5. What is the impact of increasing the principal to \$15,000 at the same interest rate?

**Tip:** Compounding more frequently (e.g., monthly vs. quarterly) leads to higher interest earned over time due to the effect of "interest on interest."

Calculate the interest earned on a $12,000 deposit at 10% annual interest compounded quarterly over 7 years. This problem demonstrates the compound interest formula and how exponential growth impacts savings. Suitable for high school students learning about finance and interest calculations.

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