Fig 1.15a Generalized Cash flow diagram involving a positive uniform gradient with ‘unknown F' =

+

Fig 1.15b Cash flow diagram (positive uniform gradient) for ‘unknown F'

The future worth of the cash flow shown in Fig. 1.15a can be obtained by finding the out the individual future worth of the cash flows shown in Fig. 1.15b and then taking their sum. As already stated, the future worth of the cash flow involving an uniform series can be determined by multiplying the uniform annual amount ‘B' with the uniform series compound amount factor. The future worth (F) of the gradient series shown in Fig 1.15b can be determined by finding out the individual future worth of the gradient values (i.e. in multiples of gradient amount ‘G') at the end of different years at interest rate of ‘i' per year and then taking the sum of these individual futures values. Then ‘F' is given as follows;