(Recasts top; adds CEO comment in paragraph 3, client assets in paragraph 5, revenue and profit estimates in paragraphs 7,8)

April 15 (Reuters) - Charles Schwab's first-quarter revenue exceeded Wall Street estimates on Monday, helped by a jump in asset management fees and client assets rising to a record high, sending its shares up about 3%.

Still, overall profit at the brokerage shrank 15% to $1.36 billion on higher interest paid on client deposits and its own borrowings.

"Against an improved macroeconomic backdrop, clients entrusted us with $96 billion in core net new assets - including $45 billion in March alone," CEO Walt Bettinger said in a statement.

A rebound in markets has boosted the value of assets under management at brokerages, allowing them to pocket higher fees even if fewer clients put their money into the funds.

That helped total client assets at the Westlake, Texas-based company reach a record $9.1 trillion, up 20% year-on-year.

Asset management and administration fees, earned from managing mutual funds and exchange-traded funds, jumped 21% to $1.35 billion.

The brokerage generated a revenue of $4.74 billion in the three months ended March 31, sailing past analysts' estimates of $4.71 billion, according to LSEG data.

Its adjusted profit available to common stockholders came in at 74 cents per share, lower than 93 cents last year.

Rate hikes by the U.S. Federal Reserve have compelled companies like Schwab to increase the interest they pay on deposits - a crucial source of capital that is used to invest in interest-earning assets and give out loans.

Schwab has also taken on debt to bolster its funding, pressuring interest revenue further.

Net interest revenue - the difference between interest earned on assets and paid out on liabilities - fell 19% to $2.23 billion.

The company on average paid 1.35% on deposits in the three months ended March 31, compared with 0.73% last year. The interest rate on its borrowings from the Federal Home Loan Bank was 5.27%, compared with 5.05% a year ago. (Reporting by Niket Nishant and Mehnaz Yasmin in Bengaluru; Editing by Devika Syamnath)