9.2.4 Sinking Fund Method of Depreciation In this method of depreciation, the book value decreases at increasing rates with respect to the life of the asset. Let P = first cost of the asset, F = salvage value of the asset, 132 Engineering Economics n = life of the asset, i = rate of return compounded annually, A = the annual equivalent amount, B, = the book value of the asset at the end of the period t, and D = the depreciation amount at the end of the period 1. The loss in value of the asset (P - F) is made available an the form of cumulative depreciation amount at the end of the life of the asset by setting up an equal depreciation amount (A) at the end of each period during the lifetime of the asset. A = (P-F) X (A/F, i, n] The fixed sum depreciated at the end of every time period earns an interest at the rate of i% compounded annually, and hence the actual depreciation amount will be in the increasing manner with respect to the time period. A generalized formula for D, is D, = (P - F) X (A/F, i, n) X (F/P, i, 1 - 1) The formula to calculate the book value at the end of period t is B, = P - (P-F) (A/F, i, n) (F/A, 1, 1) The above two formulae are very useful if we have to calculate D, and B, for any specific period. If we calculate D, and B, for all the periods, then the tabular approach would be better. EXAMPLE 9.7 Consider Example 9.1 and give the calculations regarding the sinking fund method of depreciation with an interest rate of 12%, compounded annually