The uniform series compound amount factor is used to determine the future sum (F) of a known uniform annual series with uniform amount ‘A'. The cash flow diagram is shown in Fig. 1.11. This cash flow diagram states that, if a person invests a uniform amount at the end of each year continued for ‘n' years at interest rate of ‘i' per year, how much he will get at the end of ‘n' years.

Putting the value of present worth (P) from equation (8) in equation (13) results in the following;

(18)

(19)

Fig 1.11 Cash flow diagram for ‘known A' and ‘unknown F'

The factor within bracket in equation (19) is known as uniform series compound amount factor (USCAF). Hence the future worth ‘F' can be computed by multiplying the uniform annual amount ‘A' with the uniform series compound amount factor.

Sinking fund factor:

The sinking fund factor is used to calculate the annual amount ‘A' of a uniform series from the known future sum ‘F'. The cash flow diagram is shown in Fig. 1.12. This cash flow diagram indicates that, if a person wants to get a known future sum at the end of ‘n' years at interest rate of ‘i' per year, how much he has to invest every year by an equal amount.

Fig 1.12 Cash flow diagram for ‘known F' and ‘unknown A'