Putting the expressions of ‘D₁' and ‘D₂' from equation (3.38) and equation (3.40) respectively in above expression results in the following;

On simplifying the above expression;

(3.42)

Now book value at the end of 3^rd year is given by;

Putting the expressions of ‘BV₂' and ‘D₃' from equation (3.41) and equation (3.42) respectively in above expression results in;

(3.43)

Now the generalized expression for depreciation in any given year ‘m ' can be written as follows (referring to equations (3.38), (3.40) and (3.42));

(3.44)

Putting the value of ‘ A ' from equation (3.37) in equation (3.44) results in the following;

(3.45)

Similarly the generalized expression for book value at the end of any year ‘m' is given by (referring to equations (3.39), (3.41) and (3.43));

(3.46)

The expression in the square bracket of equation (3.46) is in the form of a geometric series and its sum represents the factor known as uniform series compound amount factor (stated in Module-1). Therefore replacing the expression in square bracket of equation (3.46) with uniform series compound amount factor results in;

(3.47)

Putting the value of ‘ A ' from equation (3.37) and expression for uniform series compound amount factor in equation (3.47) results in the following generalized expression for book value at the end of any year ‘m' (1 ≤ m ≤ n ).

(3.48)

In this method, the depreciation during later years is more as compared to that in early years of the asset's useful life.