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An approximate formula for pricing American options along the lines of MacMillan  and Barone-Adesi and Whaley  is presented. This analytical approximation is as efficient as the existing ones, but it is remarkably more accurate. In particular, it yields good results for long maturity options for which the existing analytical ones fare poorly. It is also demonstrated that this approximation is more accurate than the less efficient methods such as the four-point extrapolation schemesdoi:10.3905/jod.1999.319140 fatcat:nsoqmgxdb5echf3djwbqnwjom4