From equation (19), the expression for the uniform annual amount (A) can be written as follows;
 |
(20) |
The factor within bracket in equation (20) is known as sinking fund factor (SFF). Thus one can find out the annual amount ‘A' of a uniform series by multiplying the future worth ‘F' with the sinking fund factor.
The derivation of expressions for both uniform series compound amount factor and sinking fund factor is based on the fact that, the future sum ‘F' occurs at the same time as the last ‘A' of the uniform series.
The compound interest factors with details are presented Table 1.3.
Table 1.3 Interest factors (Discrete compounding) with rate of interest ‘i' (%) and number of interest periods ‘n'
Name of the factor (1) |
Abbreviation |
Functional representation |
Mathematical expression |
Given |
To find out |
| Single payment compound amount factor | SPCAF |
(F/P, i, n) |
(1+i)n |
P |
F |
| Single payment present worth factor | SPPWF |
(P/F, i, n) |
 |
F |
P |
| Uniform series present worth factor | USPWF |
(P/A, i, n) |
 |
A |
P |
| Capital recovery factor | CRF |
(A/P, i, n) |
 |
P |
A |
| Uniform series compound amount factor | USCAF |
(F/A, i, n) |
 |
A |
F |
| Sinking fund factor | SFF |
(A/F, i, n) |
 |
F |
A |
Using this information, one can easily find out the required expenditure or income i.e. may be ‘P', ‘F' or ‘A' from the know cash flows. For example if it is required to find out the uniform annual amount ‘A' of a uniform series from the know value of present worth ‘P', then multiply the capital recovery factor (CRF) i.e. 
with ‘P' to get the required uniform annual amount ‘A' (highlighted in the above table).
In addition, the use of functional representations of the compound interest factors presented in this table can be used to find out the unknown amounts. For illustration, if it is required to find out ‘A' from known ‘P', then expression for ‘A' can be written as follows;
Further the functional representation of a compound interest factor can be obtained by multiplying the other relevant compound interest factors at a given rate of interest ‘i' and number of interest periods ‘n' and is given as follows;
 |
(21) |