By Howard Schneider and Jason Lange

WASHINGTON (Reuters) - President Donald Trump's promise to balance the federal budget in a decade rests on a sustained rise to 3 percent annual economic growth that he promised in his election campaign and a vague "feedback" effect that lowers the annual government deficit by hundreds of billions of dollars.

The projections are a leap of faith that many economists and the Federal Reserve regard as unlikely in a country where the population is aging and productivity has lagged.

They also hinge on continued low interest rates, low inflation and full employment - a decade free not just of major economic shocks but of the sort of mild recession considered part of a capitalist economy's normal ups and downs.

According to the summary tables released by the administration on Monday night, the administration is assuming economic growth reaches 3 percent annually by the end of Trump's first term and stays there at least through 2027.

Actual first quarter economic growth was a weak 0.7 percent on an annualized basis, though current Fed forecasts expect about 2.1 percent growth for the year.

Economic growth is one reason the plan forecasts tax receipts growing by around 5 percent a year even as the president promises tax cuts that "will spur investment and create jobs."

Inflation is assumed to hit the Fed's 2 percent goal and stay there, compared to the Fed's current forecast of just below 2 percent for 2016. The budget assumes the unemployment rate will rise slightly from its current 4.4 percent rate and stay at a long-term average of 4.8 percent.

Without that jump in growth and the steady environment surrounding it, deficits would increase by as much as half a trillion dollars a year - around where they are now - according to administration estimates that include an "effect of economic feedback" that reduces the government's annual shortfall by an amount that grows to $496 billion by 2027.

The exact nature of the "effect of economic feedback" was not detailed in the initial documents.

LOW RATES PERSIST DESPITE HIGHER GROWTH PATH

President Barack Obama's last budget assumed 2.6 percent annual growth, and even that is considered optimistic by professional economists and the Federal Reserve. Central bankers have penciled in trend U.S. growth of around 1.8 percent over the long run.

Some Wall Street analysts, giving credit to some of Trump's possible tax cut ideas, forecast economic growth could hit 2.3 percent in 2020, according to the latest quarterly poll of forecasters by the Philadelphia Fed.

"With all due respect, the full fiscal Trump magic was never a realistic outlook," Erik Nielsen, chief economist at UniCredit, wrote in a note to clients on Sunday.

Growth since 2000 has averaged 1.9 percent in the United States; over the course of a decade the difference between that and Trump's 3 percent figure compounds to an additional $2 trillion annually that would not get spent, invested or taxed.

The administration is also assuming that interest rates remain low, with a 10-year Treasury bond rate that rises to 3.8 percent and remains there, a figure critical to projected government borrowing costs.

While the 10-year bond has averaged near that level throughout this century and is currently well below it, periods of faster economic growth generally involve higher rates because of both the likelihood of tighter monetary policy and the likely demand for U.S. securities if the economy does accelerate.

(Reporting by Howard Schneider; Editing by David Chance and Cynthia Osterman)