Why did Haman offer to pay 10,000 silver talents, no more and no less?
The Hagaos HaBach on Tosfos in Megillah (16a) explains as follows: Every Jewish male from the age of twenty and up was required to contribute one-half shekel annually to pay towards the korbonos tzibbur. Money was considered kofer nefesh - atonement for the soul (Shekolim 2a, Shemos 30:15).
The number of the Jewish people who came out of Mitzrayim was six hundred thousand, and this always remained the official count, corresponding to the six hundred thousand neshamos which descended to this mundane world.
Thus, Haman calculated that since the average lifetime of a person is seventy years (Tehillim 90:10), during a lifetime one contributes a total of twenty-five shekolim (one only starts donating from age 20).
Consequently, the entire population of six hundred thousand, over the fifty-year period of a standard lifespan, contributed a total of fifteen million shekolim (600,000 x 25 = 15,000,000). Since one ordinary kikar [talent] contains 1,500 shekolim (unlike the kikar in the Beis HaMikdosh, which was double — three thousand shekolim — see Shemos 38:24, Rashi, Bava Basra 90b), ten thousand kikar are the exact equivalent of the fifteen million shekolim of kofer nefesh monies contributed by the entire Jewish community for fifty years (15,000,000 ÷ 1,500 = 10,000).
Therefore, Haman offered this amount because he calculated it to be the precise value of the Jewish people, and thus the King would not suffer any loss with their extermination.
