1. **Problem statement:** We need to find the annual payment amount of an annuity that starts from the second year and lasts for six years, compounded annually at 5%, with a present value of 83025. 2. **Formula used:** The present value of an annuity starting at year 2 for 6 years is given by $$PV = P \times \frac{1 - (1 + r)^{-n}}{r} \times \frac{1}{1+r}$$ where $P$ is the annual payment, $r$ is the interest rate, and $n$ is the number of payments. 3. **Explanation:** The term $\frac{1 - (1 + r)^{-n}}{r}$ calculates the present value of an annuity immediate for $n$ years starting at year 1. Since the annuity starts at year 2, we discount this value one more year by multiplying by $\frac{1}{1+r}$. 4. **Substitute known values:** $r = 0.05$, $n = 6$, $PV = 83025$ 5. **Calculate the annuity factor:** $$\frac{1 - (1 + 0.05)^{-6}}{0.05} = \frac{1 - (1.05)^{-6}}{0.05}$$ Calculate $(1.05)^{-6} = \frac{1}{(1.05)^6} \approx \frac{1}{1.3401} \approx 0.7462$ So, $$\frac{1 - 0.7462}{0.05} = \frac{0.2538}{0.05} = 5.076$$ 6. **Adjust for starting at year 2:** $$5.076 \times \frac{1}{1.05} = 5.076 \times 0.9524 = 4.835$$ 7. **Find the payment $P$:** $$83025 = P \times 4.835 \Rightarrow P = \frac{83025}{4.835} \approx 17170.5$$ **Final answer:** The annual payment amount is approximately $17170.5$.