Reynolds Metals Co., of Richmond, yesterday reported a sharp increase in sales and profits for the second quarter and first six months of 1977. Federal National Mortgage Association also reported record profits.

Earnings at Reynolds, the country's second largest aluminum manufacturer, jumped to $33.7 million ($1.90 a share) compared with $20.1 million ($1.12) in the 1976 period. Sales rose to $632.7 million from $547.3 million.

In the first six months of 1977, Reynolds profits rose to $44 million ($2.45) compared with $33.4 million ($1.84) and sales increased to $1.2 billion from $1 billion.

Chairman David Reynolds said the recent quarter's gains reflected "a more favorable product mix from greater utilization of fabricating facilities and from improved margins compared with a year ago."

Federal National Mortgage, a Washington firm that supports a secondary market for home mortgages, reported record second-quarter profits of $41.2 million (70 cents a share, diluted) compared with $33.7 million (58 cents) in the 1976 period.

For the first half of the year, Fannie Mae earned a record $84 million ($1.42) compared with $62.7 million ($1.08).

The firm it earned a recond $59.7 million return on its portfolio of mortgages in the recent quarter plus $17.7 million in fees and other income of $1.5 millions.

First Maryland Bancorp., holding company for First National Bank of Maryland, reported first half earnings before securities transactions of $5.6 million ($1.57 a share) compared with $4.7 million ($1.31) in the same period last year, Second-quarter operating profits were 81 cents a share vs. 62 cents.

Ryland Group, Inc., a homebuilder based in Columbia, Md., yesterday reported second-quarter profits of $1.78 million (67 cents a share), an increase of 42 per cent over $1.25 million (47 cents) in the comparable period of 1976. Revenues jumped 50 per cent to 34.5 million.

The second-quarter gains brought Ryland's earnings for the first six months to $2.6 million (99 cents a share) compared with $2.0 million (75 cents) on a 45 per cent gain in revenues to $55 million.

Sales contracts for 698 housing units were signed in the recent quarter and Ryland's backlog of home orders on June 30 was 694 units valued at $53 million, representing a 10 per cent increase in units and 22 per cent in dollars over the mid-1976 figures.