98 MORE INTERESTFORMULAS
TJIeuniform series compound amount factor equals 1plusthe sum of(n- 1) terms of
the single payment compound amount factorn-l
(FfA;i;n) = 1 +L(FI P, i, J)
J=1(4-13)For example,(FIA,5%,4) = 1+(FIP,5%,I)+(FIP,5%,2)+(FIP,5%,3)
4.310 = 1 + 1.050 + 1.102 + 1.158
The uniform series capital recoveryfactor equals the uniform series sinking fund factor
plus i:(AIP,i,n) =(AIF,i,n)+i (4-14)
For example,
(AI P,5%, 4)=(AI F,5%, 4) + 0.05
0.2820 =0.2320 + 0.05
This may be proved as follows:
(AIP,i,n) =(AIF,i,n)+i
[i(1 +i)n
] [1
]
(1 +i)n- 1 = (1 +i)n- 1 +lMultiply by (1 +i)n- 1 to get
ArithmeticGradient
It frequently happens that the cash flow series is not of constant amountA.Instead, there is
a uniformly increasing series as shown:t
0-1-2-3-4-5
t