Cash Flow Table 2. Standard Cash Flow Factors Machinery's Handbook, 31st Edition
148
Symbol
Formula
Symbol
P t =0
F t = n
F P 1 i + ( ) n =
P t =0
F t = n
F 1 i + ( ) n = ---------
P
P t =0
A each
n
i 1 i + ( )
1 i + ( ) n – 1 = --------------
A P
t = 1 P t =0
t = n
A each
n – 1
1 i + ( )
i 1 i + ( ) n = --------------
P A
t = 1
t = n
A each
F t = n
i 1 i + ( ) n – 1 = --------------
A F
t = 1
t = n
A each
F t = n
n – 1
1 i + ( )
i = --------------
F A
t = 1
t = n
P t =0
G 2
( n −1) G
1 i + ( ) n -------------- n – 1 i 1 i + ( )
G
1 i --
n 1 i + ( ) n – ---------
P G =
t = 2
t = n
F t = n
G 2
( n −1) G
G
1 i + ( ) i -------------- n – n – 1
1 i --
F G =
t = 2
t = n
A each
G 2 G
( n −1) G
1 i --
n 1 i + ( ) n – 1 – --------------
A G =
t = 1 t = n Example: A rental property pays $2,000/month with a $10 per month increase starting the second year. Based on a 10-year period and 8% annual interest, compute the uniform average annuity A from the rental of this property, considering the gradient. t = n t = 2 Solution: The gradient G = $10 per month; the interest each month is 1/12 of the rate i = 0.08; the duration n =120 months (using the basis of the annuity, which is monthly rent). G 1 i -- n 1 i + ( ) n – 1 – -------------- A + = 10 ------1------ 120 1+ ( ) 120 – 1 – ------------------------- + 2000 = 516+2000 = = $2,516 A initial (.08/12) (.08/12) 10(150 – 98.39) =
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