1. **State the problem:** Alexandra wants to find the present amount to deposit today to allow withdrawals of 1149 at the beginning of every 3 months for 2 years, with an interest rate of 3.20% compounded semi-annually. 2. **Identify the type of problem:** This is a present value of an annuity due problem because withdrawals happen at the beginning of each period. 3. **Given data:** - Payment per period, $R = 1149$ - Number of years, $t = 2$ - Payments every 3 months, so number of payments per year $= 4$ - Total number of payments, $n = 4 \times 2 = 8$ - Annual nominal interest rate, $i_{nom} = 3.20\% = 0.032$ - Compounded semi-annually means 2 compounding periods per year. 4. **Find the effective interest rate per payment period:** - Semi-annual interest rate $= \frac{0.032}{2} = 0.016$ - Since payments are quarterly (every 3 months), but compounding is semi-annual (every 6 months), we need the effective quarterly rate. - Effective semi-annual factor: $1 + 0.016 = 1.016$ - Effective quarterly rate $i = \sqrt{1.016} - 1 = 1.016^{0.5} - 1 \approx 0.007968$ 5. **Formula for present value of an annuity due:** $$ PV = R \times \frac{1 - (1 + i)^{-n}}{i} \times (1 + i) $$ 6. **Calculate:** - Calculate $(1 + i)^{-n} = (1.007968)^{-8} \approx 0.9385$ - Calculate numerator: $1 - 0.9385 = 0.0615$ - Divide by $i$: $\frac{0.0615}{0.007968} \approx 7.715$ - Multiply by $(1 + i)$: $7.715 \times 1.007968 \approx 7.777$ - Multiply by $R$: $7.777 \times 1149 \= 8933.37$ 7. **Answer:** Alexandra should deposit approximately $8933.37$ today to provide the payments. **Final answer:** $\boxed{8933.37}$