1. **State the problem:** Calculate the present value (PV) of receiving 10000 per year for 5 years, starting in 2 years, with an interest rate of 9%. 2. **Formula used:** The present value of an annuity starting at a future time is given by $$PV = \sum_{t=1}^{n} \frac{C}{(1+r)^{t+d}}$$ where $C$ is the payment, $r$ is the interest rate, $n$ is the number of payments, and $d$ is the delay before the first payment. 3. **Identify values:** - $C = 10000$ - $r = 0.09$ - $n = 5$ - $d = 1$ (since first payment is in 2 years, payments start at year 2, so delay $d=1$ because $t$ starts at 1) 4. **Calculate PV:** $$PV = \sum_{t=1}^{5} \frac{10000}{(1.09)^{t+1}} = 10000 \sum_{t=1}^{5} (1.09)^{-(t+1)}$$ 5. **Rewrite sum:** $$\sum_{t=1}^{5} (1.09)^{-(t+1)} = (1.09)^{-2} + (1.09)^{-3} + (1.09)^{-4} + (1.09)^{-5} + (1.09)^{-6}$$ 6. **Calculate each term:** - $(1.09)^{-2} = \frac{1}{1.09^2} = \frac{1}{1.1881} \approx 0.8417$ - $(1.09)^{-3} = \frac{1}{1.09^3} = \frac{1}{1.2950} \approx 0.7716$ - $(1.09)^{-4} = \frac{1}{1.09^4} = \frac{1}{1.4116} \approx 0.7074$ - $(1.09)^{-5} = \frac{1}{1.09^5} = \frac{1}{1.5386} \approx 0.6499$ - $(1.09)^{-6} = \frac{1}{1.09^6} = \frac{1}{1.6771} \approx 0.5963$ 7. **Sum terms:** $$0.8417 + 0.7716 + 0.7074 + 0.6499 + 0.5963 = 3.5669$$ 8. **Calculate PV:** $$PV = 10000 \times 3.5669 = 35669$$ **Final answer:** The present value of the Martian windfall today is approximately 35669.