1. : www.innovation-research.org

2. : . , - . ? . 1 000 . , . , 10% - . , . - , . , . . , - . 1 000. . 10% 1 100 . 1 000 . 1 100 . . , . , . . , , . , , , . www.innovation-research.org 3. : , , , . ( ) PV ( . Present Value), FV ( . Future value), t ( . Time) r ( . Rate). (r) (t). (PV) (FV) (r) (t) , 1 000 . . 10%. 100 . (10% 1 000 .). (PV), 1 000 . (FV) 1 100 . (t) , (r) e 10%. , . . www.innovation-research.org 4. : . , , .? : I = PV r tI = ( ) PV = ( )r = t = ( ) (FV) . : 1 000 . 3 , 8%. ? . www.innovation-research.org 5. : PV = 1 000 0 1 2 3r= 8%PV 1 000 FVt=3 FV= - , . . 8% 80 . (8% 1 000 .). 240 . (3x80). 1 000 , . , 8% 1 000 . 80 . , . :I = PV r tI = 1000 0.08 3I = 240 1 240 . FV PV + I= FV = PV + ( PV r t ) FV PV (1 + r t )= FV= 1000 (1 + 0.08 3) FV = 1240 www.innovation-research.org 6. : : FV PV (1 + r t )= - (PV). . . 15 000 . 9 . . 6.05% , 9 15 000 .? .15000 = (1 + 0.0605 9 / 12 ) PV15000 = PV (1.045375 ) PV = 15000 / 1.045375 PV = 14348.92 :FV PV =(1 + r t ) www.innovation-research.org 7. : 1 000 . 1 100 . 5.8%?FV PV (1 + r t ) = 1100 = 1000 (1 + 0.058 t )1100 / 1000 =1 + 0.058 t 1 + 0.058 t 1.1 = = 0.058 t 0.1t = 1.72 1 000 . 1 250 . ?FV PV (1 + r t ) = = 1000 (1 + r ) 1250 1.25= 1 + rr = 25% www.innovation-research.org 8. : , , (PV) . , ? . . , . . , (FV), . 100 . 10% . , (FV)? PV=0 1r= 10% PV FV 100t=1 FV = 100 www.innovation-research.org 9. : 110 . .? 100 . (PV) (100x0.10) = 10 . 100 . 110 . 10 . , . . 100 . 10 . 110 . ? , 121 . (110 x 0.10). 121 . 110 . 10% 100 . . 121 . . 100 ., 10 . , , 10 ., 1 , , 10 ., , . 10 . 1 . (10 x 10%). - , 100 . 10%, . , 100 . , , . 10 . , . . www.innovation-research.org 10. : : PV = 100 0 1 2r = 10%PV FV 100 t=2x1.10 x1.10110 FV =121 110 1.1 == (100 1.1) 1.1 =100 (1.1 1.1 ) = 100 1.12 = 100 1.21 : t = PV (1 + r ) FV www.innovation-research.org 11. : (1 + r ), (1 + 0.10) = 1.1 o . t 2(1 + r ) =1 + 0.10 )(=1.21 FV = 1000 1.21 FV = 121 5 000 . 8 7%. FV.PV = 5 000 0 1 2 3 4 5 6 7 8PV 5 000 FV r = 7%t=8 t = PV (1 + r ) FVFV == 5000 (1 + 0.07 )FV 8 FV = 8590.93 www.innovation-research.org 12. : Excel 2010 www.innovation-research.org