(Reuters) - BNY's profit jumped 16% in the third quarter on higher investment services fees as assets under its custody and administration exceeded the $50 trillion mark for the first time, the world's largest custodian bank said on Friday.

The bank's fees, typically calculated as a percentage of the assets under custody, benefited from a market rally that boosted their value as well as acquisition of new clients.

Economic resilience and expectations of an interest rate cut cycle, which began in the final month of the quarter, prompted clients to keep up their investment activities and bolstered BNY's bottom line.

Net interest income (NII) - the spread between earnings from assets and costs on liabilities - also jumped 3% as yields from BNY's bond investments offset the impact of higher deposit costs. Analysts had expected a 1.3% drop in NII, according to estimates compiled by LSEG.

Profit applicable to BNY shareholders was $1.11 billion, or $1.50 per share, for the three months ended Sept. 30, compared with $958 million, or $1.23 per share, a year earlier.

Assets under custody and administration were $52.1 trillion, 14% higher than last year.

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Total fee revenue grew 5% from a year earlier to $3.40 billion. Asset servicing - the unit responsible for safekeeping and settlement of trades - fetched 5% higher revenue.

Meanwhile, issuer services, which caters to clients issuing securities, saw a 1% jump.

As a crucial intermediary in the financial system, the 240-year-old bank's results are significant because they often reflect broader market trends.

"Our actions to run our company better, including our ongoing transition to a platforms operating model, are starting to deliver progress toward our medium-term financial targets and additional capacity to reinvest for growth," CEO Robin Vince said.

So far this year, BNY's shares have gained 43% while peers State Street and Northern Trust are up 15% and 8%, respectively.

(Reporting by Niket Nishant and Manya Saini in Bengaluru; Editing by Krishna Chandra Eluri)