He was educated at Eton, University of Tours, the School of Languages Hamburg, University College, Oxford, and Harvard Business School. Schroder joined the commercial banking and corporate Finance division of J. Henry Schroder Wagg & Co. in 1960, and was appointed a Director of Schroders in 1963. Schroder is a non-executive Director of Schroder's and a member of the company's nominations committee.
Schroder married in 1969, to Piffa, and though the couple are separated, they are not divorced; due to his wife's Roman Catholic beliefs. The couple have a daughter. Schroder flies his private plane and is a keen breeder of Middle White pigs on the Dunlossit Estate. Schroder has funded the Islay lifeboat and sponsored the island's Highland games, the Argyllshire Gathering. Schroder also helped restore an old whisky distillery on Islay.
Schroder was one of a number of wealthy individuals who cashed a cheque for 97 pence sent to them by Bizarre magazine in 2001.
Schroder received an honorary doctorate from Heriot-Watt University in 2012