Answer: Investment 2.

## Detailed Explanation We need to calculate the present value (PV) of each investment using a 10% discount rate. ### Investment 1: - 20 annual payments of $50,000 - Starting one year from today (ordinary annuity) - PV = PMT × [1 - (1 + r)^(-n)] / r - PV₁ = $50,000 × [1 - (1.10)^(-20)] / 0.10 - PV₁ = $50,000 × [1 - 0.148644] / 0.10 - PV₁ = $50,000 × [0.851356] / 0.10 - PV₁ = $50,000 × 8.51356 - **PV₁ = $425,678** ### Investment 2: - 25 annual payments of $45,000 - Starting today (annuity due) - PV = PMT × [1 - (1 + r)^(-n)] / r × (1 + r) - PV₂ = $45,000 × [1 - (1.10)^(-25)] / 0.10 × (1.10) - PV₂ = $45,000 × [1 - 0.092296] / 0.10 × 1.10 - PV₂ = $45,000 × [0.907704] / 0.10 × 1.10 - PV₂ = $45,000 × 9.07704 × 1.10 - PV₂ = $45,000 × 9.984744 - **PV₂ = $449,313** ### Investment 3: - Infinite annual payments of $40,000 - Starting one year from today (perpetuity) - PV = PMT / r - PV₃ = $40,000 / 0.10 - **PV₃ = $400,000** ### Comparison: - PV₁ = $425,678 - PV₂ = $449,313 (highest) - PV₃ = $400,000 Therefore, **Investment 2 has the highest present value**. **Key Formulas Used:** 1. Ordinary Annuity: PV = PMT × [1 - (1 + r)^(-n)] / r 2. Annuity Due: PV = PMT × [1 - (1 + r)^(-n)] / r × (1 + r) 3. Perpetuity: PV = PMT / r

Author: LeetQuiz .