The expression in the bracket is a geometric sequence with first term equal to (1+i)^-1 and common ratio equal to (1+i)^-1. Then the present worth (P) is calculated by taking the sum of the first‘n' terms of the geometric sequence (at i ≠ 0) and is given by;

(12)

The simplification of equation (12) results in the following the expression;

(13)

The factor within the bracket in equation (13) is known as uniform series present worth factor (USPWF). Thus if the value of ‘A' in the uniform series is known, then the present worth P at interest rate of ‘i' (per year) can be calculated by multiplying the uniform annual amount ‘A' with uniform series compound amount factor.

The present worth (P) of a uniform annual series of known ‘A' can also be calculated in the following manner;

Dividing both sides of equation (10) by (1+i) results in the following equation;

(14)

Subtracting equation (14) from equation (10) results in the following expression;

(15)

Equation (14) can be rewritten as;

(16)

Multiplying both sides of equation (15) by (1+i)/i and further simplification results in the following expression for the present worth ‘P';