Engineering Economic Analysis

,.

Geometric Gradient 107

:

A A 2 __ -A3

-;---r--- f

O-1-2-3-..t---n-l-n

I

p

In the general case, wherei=f g,Equation 4-24 may be written out as follows:

P=Al(1 +i)n-I +Al(1 + i)-I (~::) +Al(1 + i)-I (~::) 2

(

1 +

)

n-I

+... +Al(1+ i)-I 1+: ,

Leta=Al(1 + i)-I andb=(1 +g)/(1 +i).Equation 4-26 becomes

P =a+ ab+ ab2+... +abn-I

Multiply Equation 4-27 byb:

b P =ab+ab2+ab3+... +abn-I+abn

Subtract Equation 4-28 from Equation 4-27:

P- bP=a- abn

P(1 - b)=a(1- bn)

P= a(1- bn)

I-b

Replacing the original values foraandb,we obtain:

where i =f g.

(4-26)

(4-27)

(4-28)

(4-29)