The single payment present worth factor is used to determine the present worth of a known future worth (F) at the end of “n” years at a given interest rate ‘i' per interest period.

The present worth (P), future worth (F) and the total interest period ‘n' years are shown in Fig. 1.8.

From equation (7), the expression for the present worth (P) can be written as follows;

(8)

Fig 1.8 Cash flow diagram for ‘known F' and ‘unknown P'

The factor 1/(1+i)ⁿ in equation (8) is known as single payment present worth factor (SPPWF). Thus if future worth (F) at the end of‘n' years is known, the present worth (P) at interest rate of ‘i' (per year) can be calculated by multiplying the future worth with the single payment present worth factor.

Uniform series present worth factor (USPWF):

The uniform-series present worth factor is used to determine the present worth of a known uniform series. Let ‘A' be the uniform annual amount at the end of each year, beginning from end of year ‘1' till end of year ‘n' .

The known ‘A', unknown ‘P', and the total interest period ‘n' years are shown in Fig. 1.9. This cash flow diagram refers to the case; if a person wants to get the known uniform amount of return every year, how much he has to invest now.

The present worth (P) of the uniform series can be calculated by considering each ‘A' of the uniform series as the future worth. Then by using the formula in equation (8), the present worth of these future worth can be calculated and finally taking the sum of these present worth values.

Fig 1.9 Cash flow diagram for ‘known A' and ‘unknown P'

The present worth (P) of the uniform series is given by;

(9)

(10)

(11)