International Bank, the District based merchant bank, yesterday reported flat profits of $2.93 million (23 cents a share) for the second quarter compared with $2.85 million (24 cents) for the same period in 1980.

Profits before translation into U.S. dollars rose to $3.5 million from $2.4 million last year, and the company emphasized that losses because of rates of exchange would occur only if International Bank liquidated its assets.

"Accordingly, the true measure of our performance is in the earnings from operations, which for the second quarter of 1981 were 47 percent higher than last year, an increase of more than $1 million," said George Olmsted, the bank's chairman.

First-half profits before translation were $7.6 million (60 cents) compared with $7.8 million (64 cents) a year earlier. After conversion to U.S. dollars, profits for the six months were $6.6 million (52 cents) compared with $7.7 million (63 cents) for the same period last year.

In other reports, the mutual funds of T. Rowe Price Inc. reported second-quarter declines that the company attributed to weakenesses in the energy and technological sectors.

T. Rowe Price New Horizons Fund reported a 1 percent decline in net asset value, while the Baltimore company reported assets in its Growth Stock Fund declined by 4.9 percent. The company's New Era Fund dropped by 8.9 percent.