You invested a certain amount of money in an account which paid you $346 in simple interest at a rate of 3.8% over the course of 4 years. How much did you invest? Round your answer to the nearest cent.

To find out how much was invested, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest earned ($346),
- $ P $ is the principal amount (the initial investment, which we're trying to find),
- $ r $ is the annual interest rate (3.8% or 0.038 as a decimal),
- $ t $ is the time in years (4 years).

We rearrange the formula to solve for $ P $:

\[
P = \frac{I}{r \times t}
\]

Substituting the given values:

\[
P = \frac{346}{0.038 \times 4}
\]

Let's calculate this.

\[
P = \frac{346}{0.152} \approx 2276.32
\]

So, you invested approximately **$2,276.32**.

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

1. What would be the total amount after 4 years including the principal and interest?
2. How would the investment change if the interest rate was compounded annually instead of being simple interest?
3. What would be the interest earned if the investment was $3,000 at the same interest rate and time period?
4. How long would it take to earn $500 in interest at the same rate and principal?
5. What is the formula for compound interest, and how does it differ from simple interest?

**Tip:** Always ensure to convert percentage rates into decimals when using them in formulas.

Discover how to calculate the initial investment when given a simple interest of $346 at a rate of 3.8% over 4 years. This problem highlights the use of the simple interest formula and basic algebraic principles. Ideal for students in Grades 7-9.

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