Public and private spending for out-of-hospital prescription drugs will leap from $10.5 billion a year in 1978 to $24.9 billion in 1983 if complete drug coverage is made part of national health insurance, according to a new actuarial study released yesterday.

About half the increase would come from inflation, the rest from providing more drugs to more people.

The study was conducted by Gordon Trapnell, fellow of the Society of Actuaries and a former senior actuary for Social Security, with financing from Roche Laboratories.

Trapnell studied a range of possible options for an outpatient prescription drug program as part of a comprehensive national health insurance program.

In 1978, according to Trapnell's figures, the total public and private bill for these prescription drugs was $10.5 billion, of which 90 percent came from the private sector.

If no new programs are enacted, this figure will rise to $17.4 billion by 1983, primarily because of inflation.

The total national bill would rise because of increased use, under various options, as follows:

The United States pays most out-patient prescription drug costs exceeding 2 percent of a family's income. Coverage for entire population. Total public and private outlays in 1983 would be $18.8 billion, one-third of which paid by the U.S. government.

The United States pays costs for 18 common maintenance drugs for everybody needing them except for a $2 druggist service fee paid by patient. Overall cost, $20 billion nationally. Federal share, $9.1 billion.

Patient pays first $50 a year for drugs plus 20 percent of cost above that, United States pays the rest. Overall cost, $21.5 billion, of which U.S. share is $13 billion.

Patient pays $2 service fee, United States pays rest. Total public and private cost, $24.9 billion, of which U.S. share would be $19.9 billion.

The Carter administration national health proposal does not include outpatient prescription drugs. The bill sponsered by Sen. Edward M. Kennedy (D-Mass.) includes maintenance drugs only for aged and disabled people and would increase overall public and private outlays by $1.3 billion in 1983 beyond what it would be without program changes. However, a larger portion of existing costs would be shifted to the government.