In the televised speech announcing his fiscal plan for the District last Monday, Mayor Marion Barry said a proposed bond issue would be repaid in 30 years at a cost of "about $20 million each year." In a written message released at the same time, he said the cost would be "just over $19 million a year."

The actual cost will depend on interest rates at the time the bonds are sold, but the unexplained million-dollar discrepancy -- which could add up to $30 million -- epitomizes one of Barry's biggest difficulties in winning support for his plan from Congrees, the City Council and the public: the crediblity of his figures.

Numbers that cannot be reconciled, conflicting figures for the same calculations, unresolved differences in analysis, unsupported estimates and what appear to be plain arithmetical errors have aroused the skepticism of the very people the mayor is trying to persuade.

Even before questions were raised about the numbers, Barry encountered skepticism about his management of the budget crisis by failing to show that he had achieved the cuts in current spending he had promised. He said he would reduce this year's expenditures by $26 million, but last week his aides said they could document only $10 million in reductions.

As a result, city officials complain that questions from Congress, the council and the press focus on specific numbers instead of the over-all scope and implications of the budget problem. And Barry's critics say that his fourth and latest plan -- billed as definitive -- raises as many, questions as it answers.

"The numbers are real. They were developed by independent auditors, and we can't wish them away," Barry insisted at a hearing on Capitol Hill last week.

But City Auditor Matthew S. Watson, one of the most prominent skeptics, said he was "concerned that funding is being requested for liabilities which, while they actually exist, are unlikely to become due."

"I fear that we will collect taxes from the public in order to hoard reserves against very unlikely possibilities for payment," said Watson, the chief money-watcher for the City Council.

Key members of Congress have expressed doubts about the caculations and statistics in Barry's report on the extent of the fiscal crisis and his proposals to cope with it. Sen. Patrick J. Leahy (D-Vt.), chairman of the Senate District Appropriations Subcommittee, for example, said he wants "numbers that can be universally accepted."

The city's finances are never frozen at any one point -- money is always coming in and going out, changes in income and sales patterns affect revenues, seasonal fluctuations affect balances -- but there still is open skepticism about Barry's calculations.

Many of the apparent discrepancies can be explained by members of Barry's staff, but in the aggregate, they have not made it easier for the mayor to win acceptance of his proposals.

The problem areas in his plan and its accompanying charts and tables show up in all aspects of it; caculations of the deficit, revenue projections, future spending and the size of the payroll.

One table, for example, shows a projected budget of $1.502 billion for the 1981 fiscal year starting Oct. 1 at current levels of staffing and services, or of $1.441 billion at reduced levels. Neither figure is the same as that in the city's official proposed 1981 budget as amended, currently before Congress, which puts estimated spending at $1.521 billion -- an $80 million difference.

The plan's budget projections for 1982 and 1983 include $30 million to be set aside out of operating revenues as a "contingency reserve." There is no explanation of where this money would come from in a time of fiscal hardship or why it is needed. No such reserve exists now, and Congress always has been reluctant to authorize the city to put aside funds not earmarked for specific purposes.

One of the most elusive numbers is the size of the city's payroll. The official figure as of June 30, according to budget office statistics, was 31,326 workers. The 1981 budget, as amended, shows an anticipated work force of 31,466, which would, improbably, represent an increase.

A chart included in the plan document shows the projected payroll at the end of the 1981 fiscal year as 29,462; elsewhere, the text says that "the employment base for appropriated positions during FY 1983 is expected to be about 28,000 employes."

In his written message, Barry said that "the work force" will be reduced by an additional 2,100 positions in 1982 . . . one top of the 2,460 work force reduction to be achieved in 1981."

Subtracting those two figures from the current number of employes yields a projected work force of 26,766 at the end of the 1982 fiscal year -- more than a thousands fewer than the plan projects for 1983.

There appears to be no single explanation for this variety of estimates. City officials and the District's auditors said that anticipated cutbacks already have overtaken the staffing figures in the proposed 1981 budget. Moreover, they say, the rapid buildup of pressure on Barry to balance future budgets has led him to envision deeper cuts than those listed in charts drafted some months ago.

In addition, they said, some discrepencies were to be expected in a thick document full of figures prepared quickly.

One number in Barry's message that drew immediate questions from members of Congress and the council was the $215 million in "needed cash" that the mayor proposes to borrow through the federal government.

There is no explanation for that number in the text of the plan or in the mayor's speech, nor any breakdown of what the money would be used for.

City Administrator Elijah B. Rogers said later that it represented the sum of the projected operating deficit for this fiscal year, $125 million, plus that portion of the official $284 million cumulative deficit that represents current liabilities -- $90 million.

But the $125 million figure for the current deficit is itself problematical.

A chart in the plan document says it equals the differences between total anticipated revenues this year of $1.287 billion and expenditures of $1.412 billion.

However, Congress only authorized the District to spend $1.38 billion in appropriated funds this year -- which indicates that expenditures will exceed not only revenues but also legal permissin to spend. According to Watson, the city auditor, this is a "possible violation" of federal law.

Another problem with the $125 million deficit figure is that the plan explains the events that caused it but does not assign any dollar values to them.

Rogers said $35.6 million of it is "underfunding" of programs -- a phrase that critics said is a euphimism for overspending.

Another $28.5 million, he said, is attributable to the "changover" from a cash system of accounting to an accrual system of accounting.

Rogers acknowledged with a laugh yesterday that it is difficult to convince people that this number represents actual cash that has to be raised.

The thing to keep in mind, he said, is that "we are going to be paying 1980 bills with money that is earmarked for 1981 bills, and sooner or later it is going to have to stop."