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1.Future Value

1.Future Value. F. F = P( F/P , i , n). 0 1 2 3 n-1 n. 2.Present Value . F. F = P( F/P , i , n). 0 1 2 3 n-1 n. 0 1 2 3 n-1 n. 3 ) Uniform Series to Present Worth. P = A( P/A , i , n) A = P( A/P , i , n) .

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1.Future Value

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  1. 1.Future Value F F = P( F/P , i , n) 0 1 2 3 n-1 n

  2. 2.Present Value F F = P( F/P , i , n) 0 1 2 3 n-1 n

  3. 0 1 2 3 n-1 n 3) Uniform Series to Present Worth P = A( P/A , i , n) A = P( A/P , i , n)

  4. 4) Uniform Series to Future Worth F 0 1 2 3 4 n-1 n F = A( F/A , i , n) A = F( A/F , i , n)

  5. 5) Gradient 0 1 2 3 4 n-1 n= 0 1 2 3 4 n-1 n + 0 1 2 3 4 n-1 n g 2g 3g (n-2)g n-1g g 2g 3g (n-2)g n-1g

  6. ตัวอย่างการคำนวณ 2.1) F P 0 1 2 3 4 23 24 F = 12,000 ( F/P , 8% , 24yr) = 12,000(6.3412)

  7. 2.2) a F P 50,000 P = 50,000 ( F/P , 20% , 3yr) = 50,000(0.5787) 0 1 2 3 4 5 b 50,000 P = 50,000 ( P/F , 20% , 3yr) = 50,000(0.5787) -3 -2 -1 0

  8. 2.3) -5 -4 -3 -2 -1 0 1 2 3 4 5 300 400 F3 F2 F1 600 F = F1 + F2 + F3 = 600 (F/P , 5% , 10yr) + 300 (F/P , 5% 8yr) + 400 (F/P , 5%, 5yr)

  9. 2.4) P F 600 600 600 600 600 0 1 2 3 4 9 P = 600 ( P/A), 16% , 9 , yr) = 600 ( 4.6065)

  10. 2.5) F A A A A A 0 1 2 3 4 8 F = 1 (F/A , 14% , 8 yr) = 1 (13.2328) = 13.232M

  11. 2.6) A A A A A 0 1 2 3 4 7 A = 6,000( A/F , 5 1 /2 % , 7yr) = 6,000 (0.12282 + 0.11914) 2 = 6,000 (.12098) A = 725.88

  12. 2.7) 0 1 2 3 9 10 = 0 1 2 9 10 + 0 1 2 3 9 10 5,000 5,500 6,000 85,000 9,000 5,000 500 1,000 4,000 5,000 P = P1 + P2 = 5,000 (P/A , 10% , 10yr) + 500 (P/G , 10% , 10 yr = 5,000 (6.1446) + 500 (22.8913

  13. 2.8) 0 1 2 3 7 8 = 0 1 2 3 7 8 + 0 1 2 3 7 8 60,000 200,000 2,000 2g8g 9gt 80,000 160,000 18,000 2,000 A = 200,000 – 20,000(A/G, 12%) 8yr)

  14. 2.9) 0 1 2 3 4 5 6 7 8 5,000 P = -5,000 - [500 (P/A , 8% , 6 yr)] (P/F , 8% , 2yr = -5,000 - [ (500) (4.6229) ] (0.8573)

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