Sprague was born in
London the son of Thomas Sprague, a wholesale stationer. He attended Tarvin Hall School near Chester. Sprague was an undergraduate at
St John's College, Cambridge, where he was elected to a fellowship following his ranking as
Senior Wrangler in the
Cambridge Mathematical Tripos of 1853. He was awarded the
Smith's Prize of Cambridge University in the same year. After serving as the actuary to the
Equity and Law life insurance company (1861–1873), he became chief executive (1873–1900) of the
Scottish Equitable Life Assurance Society in Edinburgh. In 1874 he was elected a Fellow of the
Royal Society of Edinburgh. His proposers were David Smith,
Samuel Raleigh,
Philip Kelland, and
Peter Guthrie Tait. He died on 29 November 1920 at West Holme in
Woldingham in
Surrey. ==Memorials==