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Answer (2)
Answer: 1. Future Value (FV): 650,000 2. Annual Interest Rate (r): 12% = 0.12 3. Monthly Interest Rate: 0.01 4. Quarterly Interest Rate: 0.030301 5. Total Number of Quarters (n): 8 Using the formula: P = FV × r / [(1 + r)^n - 1] P = 650,000 × 0.030301 / [(1 + 0.030301)^8 - 1] Calculating: P = 650,000 × 0.030301 / [0.292256] P ≈ 67,322.64 Regular Payment: Approximately 67,322.64 per quarter.Step-by-step explanation:1. Identify the Future Value (FV): FV = 650,0002. Determine the Annual Interest Rate (r): Annual interest rate = 12% = 0.123. Calculate the Monthly Interest Rate: Monthly interest rate = 0.12 / 12 = 0.014. Calculate the Quarterly Interest Rate: Quarterly interest rate = (1 + 0.01)^3 - 1 Quarterly interest rate ≈ 0.0303015. Determine the Total Number of Quarters (n): Total number of quarters = 2 years × 4 quarters/year = 8 quarters6. Set up the formula for the future value of an annuity: FV = P × [(1 + r)^n - 1] / r7. Rearrange the formula to solve for P (regular payment): P = FV × r / [(1 + r)^n - 1]8. Substitute the known values into the formula: P = 650,000 × 0.030301 / [(1 + 0.030301)^8 - 1]9. Calculate the denominator: First, calculate (1 + 0.030301)^8: (1 + 0.030301)^8 ≈ 1.292256 Then, subtract 1: 1.292256 - 1 ≈ 0.29225610. Substitute back into the formula: P = 650,000 × 0.030301 / 0.29225611. Calculate the numerator: 650,000 × 0.030301 ≈ 19,695.6512. Calculate P: P ≈ 19,695.65 / 0.292256 ≈ 67,322.6413. Final Result: Regular Payment: Approximately 67,322.64 per quarter.
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