Calculate the present value of a contract with varying annual payments and its equivalent constant annual payment.

The formula for the present value of a single future payment is $PV = \frac{FV}{(1+r)^n}$, where $FV$ is the future value, $r$ is the discount rate, and $n$ is the number of years. The discount rate $r = 10\% = 0.10$.

• For Year 1 (₦8,000): $$PV_1 = \frac{8000}{(1+0.10)^1} = \frac{8000}{1.10} \approx 7272.73$$
• For Year 2 (₦9,000): $$PV_2 = \frac{9000}{(1+0.10)^2} = \frac{9000}{1.21} \approx 7438.02$$
• For Year 3 (₦10,000): $$PV_3 = \frac{10000}{(1+0.10)^3} = \frac{10000}{1.331} \approx 7513.15$$
• For Year 4 (₦11,000): $$PV_4 = \frac{11000}{(1+0.10)^4} = \frac{11000}{1.4641} \approx 7513.15$$

The total present value is the sum of the present values of all individual payments.

$$Total PV = PV_1 + PV_2 + PV_3 + PV_4$$ $$Total PV = 7272.73 + 7438.02 + 7513.15 + 7513.15$$ $$Total PV = 29737.05$$

The PVIFA for an ordinary annuity is given by the formula:

$$PVIFA = \frac{1 - (1+r)^{-n}}{r}$$

Given $r = 0.10$ and $n = 4$ years:

$$PVIFA = \frac{1 - (1+0.10)^{-4}}{0.10}$$ $$PVIFA = \frac{1 - (1.10)^{-4}}{0.10}$$ $$PVIFA = \frac{1 - 0.683013455}{0.10}$$ $$PVIFA = \frac{0.316986545}{0.10} \approx 3.169865$$

To find the constant annual payment $A$, we set the total present value of the contract equal to the present value of an annuity and solve for $A$:

$$Total PV = A \times PVIFA$$ $$A = \frac{Total PV}{PVIFA}$$ $$A = \frac{29737.05}{3.169865}$$ $$A \approx 9380.54$$

The amount quoted by the contractor should be ₦9380.54 per year.

The final answer is $\text{₦9380.54}$.