Chase-Manhattan Bank, the nation's third-largest bank, reported yesterday that its second-quarter profits fell 2 percent from last year's record level.

Chase said its earnings before securities transactions fell to $100.6 million ($2.83 a share) from $103 million ($3.04) in the second quarter of 1980. Earnings for the first six months of the year, Chase said, were $168.8 million ($4.67), off 10.9 percent from earnings of $189.6 million ($5.58) in the same period in 1980.

Merrill Lynch & Co., the nation's largest investment firm, said its earnings for the second quarter rose a record 4 percent from 1980, due to near-record volume in stock trading and increased volume in options and commodities trades.

Merrill Lynch said its profit rose to $67.7 million on revenues of $1 billion from $65.2 million on revenues of $765 million in the second quarter of 1980. per-share earnings fell from $1.79 a share last year to $1.72 a share because there were 10 percent more shares outstanding this year.

For the first half, Merrill Lynch's earnings reached $113 million ($2.89), a 13 percent gain, from $99.7 million ($2.74) for the first six months of last year. First-year revenues rose 31 percent to $1.9 from $1.5 billion last year.

Time Inc., the nation's largest magazine publisher, reported second-quarter earnings of $49.2 million ($1.60), up 18 percent from $41.6 million ($1.49) in the same period a year ago. The company attributed the result to strong gains in magazine publishing, video and forest products.

Second-quarter revenues rose 23 percent to $858 million from $696.6 million.Last year's second-quarter profit was before a loss of $917,000 from discontinued operations, making final net income $40.7 million ($1.45). Second-quarter revenues rose 23 percent to $858 million from $696.6 million.

In the first half of the year, Time said, income from continuing operations was $86.7 million ($2.87) on revenues of $1.6 billion, up from earnings of $70.8 million ($2.51) on last years' first-half revenues of $1.4 billion -- a 14 percent increase.