1. **State the problem:** We need to find the discounted value of payments of 1012 made every six months for 8 years, with an interest rate of 5% per annum compounded quarterly. 2. **Identify the formula:** The discounted value of an annuity is given by the formula $$PV = P \times \frac{1 - (1 + i)^{-n}}{i}$$ where $P$ is the payment per period, $i$ is the interest rate per period, and $n$ is the total number of payments. 3. **Calculate the interest rate per period:** The nominal annual interest rate is 5% compounded quarterly, so the quarterly interest rate is $$i_q = \frac{0.05}{4} = 0.0125$$ Since payments are every six months (2 quarters), the effective interest rate per payment period is $$i = (1 + i_q)^2 - 1 = (1 + 0.0125)^2 - 1 = 1.025156 - 1 = 0.025156$$ 4. **Calculate the number of payments:** Payments are every six months for 8 years, so $$n = 8 \times 2 = 16$$ 5. **Calculate the present value:** Substitute values into the formula $$PV = 1012 \times \frac{1 - (1 + 0.025156)^{-16}}{0.025156}$$ Calculate the denominator and exponent: $$ (1 + 0.025156)^{-16} = (1.025156)^{-16} = \frac{1}{(1.025156)^{16}} \approx \frac{1}{1.488863} = 0.671668$$ Then, $$PV = 1012 \times \frac{1 - 0.671668}{0.025156} = 1012 \times \frac{0.328332}{0.025156} = 1012 \times 13.0507 = 13200.32$$ 6. **Final answer:** The discounted value of the payments is approximately **13200.32**.