### Compound Interest Calculation Example **Problem Statement:** Set up the formula to find the balance after 12 years for a total of $3,000 invested at an annual interest rate of 7% compounded daily. **Multiple Choice Options:** 1. \( A = 3000e^{(7)(12)} \) 2. \( A = 3000 \left(1 + \frac{7}{365}\right)^{(7)(12)} \) 3. \( A = 3000 \left(1 + \frac{0.07}{365}\right)^{(365)(12)} \) 4. \( A = 3000e^{(0.07)(12)} \) **Explanation of Options:** - **Option 1:** This uses the continuous compounding formula incorrectly adjusted. - **Option 2:** This option uses an incorrect interest rate in the formula. - **Option 3:** This option correctly employs the formula for daily compounding. - **Option 4:** This option is another form of continuous compounding, but properly formatted. **Correct Answer:** The correct formula for calculating the balance \(A\) with daily compounding interest is: \[ A = 3000 \left(1 + \frac{0.07}{365}\right)^{365 \times 12} \] Thus, the correct answer is **Option 3**. ### Graph and Diagram Explanation There are no graphs or diagrams present in this problem, just a multiple-choice question with mathematical formulas. ### Definitions: 1. **Compounded Daily:** Interest added to the principal balance daily. 2. **Formula Explanation:** - \( P \): Principal amount (initial investment) = $3,000 - \( r \): Annual interest rate = 7% or 0.07 - \( n \): Number of times interest is compounded per year = 365 (daily) - \( t \): Number of years the money is invested = 12 - Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \) By understanding these concepts and using the correct formula, you can accurately determine the accumulated balance of an investment.