1. **State the problem:** We want to find the future value of quarterly investments of 460 over 12 years at an annual interest rate of 6%. 2. **Formula used:** The future value of an ordinary annuity is given by $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $P$ is the payment per period, $r$ is the interest rate per period, and $n$ is the total number of payments. 3. **Identify values:** - Quarterly payment $P = 460$ - Annual interest rate = 6%, so quarterly rate $r = \frac{6\%}{4} = 0.015$ - Number of years = 12, so total quarters $n = 12 \times 4 = 48$ 4. **Calculate:** $$FV = 460 \times \frac{(1 + 0.015)^{48} - 1}{0.015}$$ 5. **Evaluate powers and subtraction:** Calculate $(1 + 0.015)^{48} = 1.015^{48} \approx 2.039887$ 6. **Substitute:** $$FV = 460 \times \frac{2.039887 - 1}{0.015} = 460 \times \frac{1.039887}{0.015}$$ 7. **Divide and multiply:** $$\frac{1.039887}{0.015} \approx 69.3258$$ $$FV = 460 \times 69.3258 \approx 31879.87$$ **Final answer:** The investment will be worth approximately $31879.87$ after 12 years.