This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
Step 1: Calculate the present value (PV) of each payment. The formula for the present value of a single future payment is PV = (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 = (8000)/((1+0.10)^1) = (8000)/(1.10) ≈ 7272.73 For Year 2 (₦9,000): PV_2 = (9000)/((1+0.10)^2) = (9000)/(1.21) ≈ 7438.02 For Year 3 (₦10,000): PV_3 = (10000)/((1+0.10)^3) = (10000)/(1.331) ≈ 7513.15 For Year 4 (₦11,000): PV_4 = (11000)/((1+0.10)^4) = (11000)/(1.4641) ≈ 7513.15 Step 2: Calculate the total present value of the contract. 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 Step 3: Calculate the present value interest factor for an annuity (PVIFA). The PVIFA for an ordinary annuity is given by the formula: PVIFA = 1 - (1+r)^-nr Given r = 0.10 and n = 4 years: PVIFA = 1 - (1+0.10)^-40.10 PVIFA = 1 - (1.10)^-40.10 PVIFA = (1 - 0.683013455)/(0.10) PVIFA = (0.316986545)/(0.10) ≈ 3.169865 Step 4: Determine the equivalent constant annual payment (annuity). 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 × PVIFA A = (Total PV)/(PVIFA) A = (29737.05)/(3.169865) A ≈ 9380.54 The amount quoted by the contractor should be ₦9380.54 per year. The final answer is ₦9380.54. Send me the next one 📸