The International Monetary Fund will be forced to borrow a substantial amount of money early in 1983 to replenish its resources, which will be seriously depleted by its large scheduled loan to Mexico.

Official figures obtained by The Washington Post show that present uncommitted ordinary resources available to the fund, plus unused lines of existing credits, are equal to 20.5 billion SDRs.

SDRs, or special drawing rights, are the special currency issued by the fund, and presently are equal to about $1.09 each.

The IMF expects that this total will be reduced from 20.5 billion to 10.5 billion SDRs by April 1983 as a consequence of a probable 4.4-billion-SDR commitment to Mexico, and even larger "normal" lending operations.

In effect, sources confirmed the thrust of a report by the Institute for International Economics earlier this week that the IMF would need some emergency infusion of money before the question of larger quotas -- basic capital funds -- is settled, for financing programs in the second half of this decade.

Treasury Undersecretary Beryl Sprinkel had challenged the institute's conclusion, citing figures approximating those of the IMF. But neither Sprinkel nor the institute had suggested that "normal" operations of the fund would drain even more from the IMF than the big Mexican bail-out. According to the fund's calculations, these other borrowings will total 5.6 billion SDRs.

In the course of providing loans totaling 10 billion SDRs to all borrowers -- including Mexico -- between now and next April, the IMF expects to exhaust its existing and uncommitted lines of credit amounting to 5.5 billion SDRs. For this purpose, the IMF doesn't count about 3.5 billion SDRs in lines of credit from the General Agreements to Borrow (GAB), which are available for use only for the rich nations belonging to the GAB.

Therefore, the IMF has concluded that it must replenish its lines of credit -- certainly by midyear -- to avoid depleting its ordinary resources below an expected level of 10.5 billion SDRs. This would enable it to meet any loan demands from the latter half of 1983 until new quotas become effective in 1985.

Saudi Arabia earlier had made a tentative commitment to lend the IMF another 4 billion SDRs next year.

Presumably the IMF would like to get that much -- and more, if possible -- from Western nations.

None of this affects the debate over IMF quotas, or deposits of currencies by member nations. Against American resistance, the IMF wants to boost the total quotas from 61 billion SDRs to between 100 billion and 120 billion SDRs. That issue will be debated at the annual meeting in Toronto early next month.