1. **Problem Statement:** Angie deposits 5378.76 at the end of every 2 months for 4 years. The fund is compounded monthly at 3% annual interest. We need to find the total amount she paid for her bag. 2. **Understanding the problem:** The deposits are made every 2 months, but interest compounds monthly. We need to find the effective interest rate per 2 months and the total number of deposits. 3. **Calculate the effective interest rate per 2 months:** Annual nominal interest rate $i_{annual} = 0.03$ (3%) compounded monthly means monthly interest rate $i_m = \frac{0.03}{12} = 0.0025$. Effective interest rate for 2 months $i_2 = (1 + i_m)^2 - 1 = (1 + 0.0025)^2 - 1 = 1.00500625 - 1 = 0.00500625$. Rounded to 6 decimal places: $i_2 = 0.005006$. 4. **Number of deposits:** Deposits every 2 months for 4 years means $n = \frac{4 \times 12}{2} = 24$ deposits. 5. **Calculate the future value of an ordinary annuity:** Formula: $$FV = P \times \frac{(1 + i)^n - 1}{i}$$ Where $P = 5378.76$, $i = 0.005006$, $n = 24$. Calculate numerator: $(1 + 0.005006)^{24} - 1 = (1.005006)^{24} - 1$. Calculate $(1.005006)^{24} = e^{24 \times \ln(1.005006)} \approx e^{24 \times 0.004993} = e^{0.119832} \approx 1.1274$. So numerator $= 1.1274 - 1 = 0.1274$. 6. **Calculate future value:** $$FV = 5378.76 \times \frac{0.1274}{0.005006} = 5378.76 \times 25.45 = 136,885.43$$ 7. **Total amount paid:** Total deposits = $5378.76 \times 24 = 129,090.24$. 8. **Answer:** The amount she paid for her bag (total deposits) is **129090.24**. Note: The future value is the amount accumulated, but the question asks how much she paid, which is the sum of all deposits.