Americans' personal income rose by one-half percent last month, a modest improvement over the 0.2 percent January gain and the biggest increase since November, the government reported yesterday.

Personal income had fallen less than 0.1 percent in December, the first decline since the 1975 recession.

The Commerce Department also reported yesterday that the nation's balance of payments--the broadest measure of international transactions--showed an $85 million deficit for the fourth quarter of last year, but a $6.6 billion surplus for all of 1981.

It was the first quarterly deficit since $500 million in red ink from April through June of 1980. The yearly surplus, however, was the largest since the 1975, when it was $18.3 billion.

And McGraw-Hill Information Systems Co. said that construction activity this year likely will be slower than anticipated five months ago because of the recent rise in interest rates and the deeper-than-expected recession.

McGraw-Hill said construction contracting this year is expected to total $165.3 billion, approximately $4 billion less than the level predicted five months ago.

But the company noted in its first update to its 1982 Dodge-Sweet's construction outlook that the forecast still is 10 percent higher than actual construction spending in 1981.

The report on personal income said it rose to a seasonally adjusted annual rate of $2.51 trillion in February.

Disposable, or after-tax, income rose one-half percent, the same as in January. Because February's rate of inflation will not be known until next Tuesday's Labor Department report of the consumer price index, the disposable income for February could not be adjusted for price hikes.

But January's one-half-percent increase in the same category translated to an actual 0.3 percent shrinkage in spending power after that month's inflation rate was figured in.

Personal consumption spending, which economists say is the best hope for pulling the nation out of recession, rose 0.8 percent in February after gaining 1.1 percent in January.

Personal savings--disposable income minus spending--fell 5.1 percent to $103 billion in February.

In its balance-of-trade report, the Commerce Department said that the fourth quarter's $9.2 billion merchandise trade deficit was offset by increases in the return on private investment overseas, improved interest payments on bank loans to foreigners and a variety of other income sources.

Through 1981, the dollar appreciated an average of 16 percent against the currencies of 10 major trading nations, the department said. graph: Personal Income for 1981-82