You deposit $5000 in an account earning 2.9% interest compounded quarterly. How much interest will you earn over 8 years? Round your answer to the nearest cent.

To calculate the interest earned on an account with compound interest, we use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial deposit), which is $5000.
- $ r $ is the annual interest rate (decimal), which is 2.9% or 0.029.
- $ n $ is the number of times the interest is compounded per year (quarterly, so $ n = 4 $).
- $ t $ is the time the money is invested for (8 years).

First, we calculate the total amount ($ A $) after 8 years and then subtract the initial deposit ($ P $) to find the interest earned.

\[
A = 5000 \left(1 + \frac{0.029}{4}\right)^{4 \times 8}
\]

Let me calculate that.The interest earned over 8 years on a $5000 deposit at an interest rate of 2.9% compounded quarterly is **$1300.32**.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the frequency of compounding affect the total interest earned?
2. What would the interest be if the rate was increased to 3.5%?
3. How much would you earn in 5 years with the same interest rate and compounding frequency?
4. What would the interest be if it was compounded monthly instead of quarterly?
5. How does simple interest compare to compound interest for the same initial deposit?

**Tip:** When interest is compounded more frequently, the total interest earned increases even if the interest rate stays the same.

Find out how much interest you can earn on a $5000 deposit with a 2.9% interest rate compounded quarterly over 8 years. This problem uses the compound interest formula to calculate the accumulated amount and the interest earned, suitable for Grades 9-12 students.

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