1. **State the problem:** We need to find the size of payments deposited at the beginning of each 6-month period in an account with 9.6% annual interest compounded semiannually, so that the future value after 14 years is 150000. 2. **Identify the formula:** Since payments 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 payments 3. **Calculate parameters:** - Annual nominal interest rate = 9.6% = 0.096 - Compounded semiannually means 2 periods per year - Interest rate per period $r = \frac{0.096}{2} = 0.048$ - Number of years = 14 - Total number of periods $n = 14 \times 2 = 28$ 4. **Plug values into the formula and solve for $P$:** $$150000 = P \times \frac{(1 + 0.048)^{28} - 1}{0.048} \times (1 + 0.048)$$ 5. **Calculate $(1 + 0.048)^{28}$:** $$ (1.048)^{28} \approx 3.6101 $$ 6. **Calculate the fraction:** $$ \frac{3.6101 - 1}{0.048} = \frac{2.6101}{0.048} \approx 54.377 $$ 7. **Calculate the entire multiplier:** $$ 54.377 \times 1.048 \approx 56.978 $$ 8. **Solve for $P$:** $$ P = \frac{150000}{56.978} \approx 2632.44 $$ **Final answer:** The payment size must be approximately **2632.44** deposited at the beginning of each 6-month period.