Consumers and businesses borrowed more money last year and paid it back on time, boosting the profits and reducing the loan losses of local banks.

Earnings increases ranging from 10 to 900 percent were reported by half a dozen local financial institutions, most of them posting record profits.

The banks said strong loan demand and a turnaround in provisions for loan losses were key factors in their increased profits.

Total loans for the year were up by amounts ranging from 11.9 percent for Equitable Bancorp. of Baltimore to 43 percent at the tiny American Bank of Maryland.

"Demand for credit continued to strengthen during the first quarter," reported Bank of Virginia Co. Richmond, which posted a 13 percent net growth. Chairman Frederick Deane, Jr. said, "The growth in loan volume accounted for the improvement in net interest income" during the quarter.

Bank of Virginia Co. reported its earnings more than doubled in the past year, setting a new record.

Income before securities transactions of $11.8 million ($2.58 a share), compared with $5.1 million ($1.02) last year, when earnings were depressed by reserves for loan losses due to foreclosure of real estate mortgages.

Bank of Virginia Co. said its provision for loan losses was $10.7 million, down from $17 million a year ago, and actual losses were $11.2 million, compared with $16.1 million.

In reporting that its assets passed the billion-dollar mark for the first time, Union Trust Bancorp. of Baltimore said, "Most of this growth occurred in loans and direct leases."

Chairman J. Stevenson Peck said loans and leases of $657 million were up 20.5 percent from 1976. He noted that a prtion of his bank's improved fourth quarter performance was due to reducing loan loss provisions from $4.1 million to $3 million.

Union Trust reported fourth quarter earnings of $1.1 million (46 cents a share), an increase of 318 percent over 1976's earnings of $274,000 (11 cents). Annual earnings for the Baltimore financial conglomerate were up 9 percent to $6.3 billion ($2.58).

The most dramatic earnings increase came from American Bank of Maryland, a Financial General subsidiary, which said earnings before securities transactions for 1977 jumped from $112,000 to $1 million, while net earnings went from $101,000 to $990,000.

"A reduction in the provisions for loan loss expense and a large increase in outstanding loans" were credited for the improvement by president G. J. Manderfield.

National Bank of Washington's annual income for 1977 grew from $4.3 million ($3.94 a share) to $5 million ($4.55), a 15 percent increase.

Total assets increased from $662 million to $775 million, while deposits climbed by $56 million to $630 million.

For the fourth quarter, National Bank of Washington reported net income of $1.6 million ($1.47), compared with $1.4 million ($1.28).

Reporting a 16 percent increase in earnings for 1977, Equitable Bancorp. of Baltimore raised its cash dividend from 48 cents to 56 cents a year, and declared an additional 4 percenr stock dividend.

Equitable reported earnings of $10.8 million before securities transactions, equivalent to $3.10 per share, the highest in its history.

The bank holding company changed its method of accounting for interest on installment loans last year. For a restated 1975 report, earnings were $9.3 million ($2.67 a share).

In the past year, loans increased 22 percent to $11 billion, and total deposits grew 15 percent to $1.48 billion for the company, which owns Equitable Trust Co. of Baltimore, Columbia Bank and Trust, Farmers and Merchants Bank of Hagerstown, University National Bank of Rockville and Truckers and Savings Bank, Salisbury.

Fourth quarter earnings were $2.9 million (84 cents), up from $2.4 million (68 cents).

National Permanent Federal Savings and Loan Assn. reported it received $53 million in new deposits and made $138 million in new loans last year, as total assets increased to $637 million.

President John W. Stadtler said "tremendous activity" in residential real estate last year will be followed by strong demand for mortgage money in 1976. Savings gains are expected to be smaller, he said, indicating some tightening of mortgage supplies.