1. **Problem statement:** Briac Steel deposits 4400 at the beginning of every month into a fund with an 8% annual interest rate compounded semi-annually. We want to find the total amount in the fund after 10 years. 2. **Formula used:** Since deposits are made at the beginning of each period, this is an annuity due. The future value of an annuity due is given by: $$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$ where: - $P$ is the payment per period, - $r$ is the interest rate per period, - $n$ is the total number of periods. 3. **Important rules:** - Interest is compounded semi-annually, so the interest rate per compounding period is $\frac{8\%}{2} = 4\% = 0.04$. - Payments are monthly, but compounding is semi-annual, so we must adjust the number of periods and rate accordingly. 4. **Adjusting periods and rate:** - Number of years = 10 - Number of semi-annual periods = $10 \times 2 = 20$ - Since payments are monthly, there are $10 \times 12 = 120$ payments. 5. **Reconciling monthly payments with semi-annual compounding:** We convert the monthly payment to an equivalent semi-annual payment by summing 6 monthly payments per semi-annual period: $$P_{semi} = 4400 \times 6 = 26400$$ 6. **Calculate future value:** $$FV = 26400 \times \frac{(1 + 0.04)^{20} - 1}{0.04} \times (1 + 0.04)$$ Calculate intermediate values: $$(1 + 0.04)^{20} = 2.191123$$ $$\frac{2.191123 - 1}{0.04} = \frac{1.191123}{0.04} = 29.778075$$ $$FV = 26400 \times 29.778075 \times 1.04 = 26400 \times 30.969198 = 817,802.07$$ 7. **Final answer:** The fund will be worth approximately **817802.07** after 10 years.