**Sinking Fund Depreciation Method**

Prior to World War II little attention was given to depreciation, and some business actually established savings accounts in which uniform annual deposits were placed so that at the end of the useful life an asset could be replaced.

Given the costs basis or the amount paid for an asset P, the salvage value at the end of the useful life F, the useful life n years, and the depreciation account paid annual compound interest of I, then the annual deposit to the depreciation account is

D = (P - F) (A|F,i%,n)

=PMT(i%, n, -()P-F)

The depreciation method based on Equation 9.1 is called the sinking fund factor. The actual depreciation for year dt is the sum of the annual deposit and the accumulated interest for year t.

dt = d(F| P,i%,t-1)

=FV(i%, t-1, -PMT(i%, nn -(P-F)))

The undepreciated portion of an asset is called the book value Bt, which based on the sinking fund depreciation is given by

Bt =P -d(F|A,i%,t)

= P -FV(i%, t, -PMT(i%, n, , -(P-F))