First novel explores the gnarled roots of the rich; Old Money, by Lacey Fosburgh. New York: Doubleday. 425 pp. $17.95.

Money? ''Spend it,'' advises the grandmother of Abigail Rushing Boarchards, ''enjoy it and give away as much as possible.'' Old money, that is. The sort of money inherited by those fortunate enough to be born on Fifth Avenue in a ''forty-room house . . . in a second-floor bedroom decorated in silk,'' who on their country estates have lakes on which, every other day, a plane lands to deliver ''crates of lobsters from Maine.''

Born with ''enough silver and china for 24 as a gift at birth,'' Abigail has always assumed she will inherit her father's share of the Boarchards fortune, although she has struggled to break free of the family. Achieving a successful career in photo-journalism, she is the first person in the family ever to have had a job, and this has bewildered and angered her relatives. She is also the first to have spent her child-hood year-round at Weather Tree, the estate built by her great-grandfather and named for a huge willow tree which died long ago - ''Of rot, they said, the kind that seeps in along the branches above and the roots below, doing its deed in secret, so no one has a way to know.''

Notified that her father has committed suicide, Abigail arrives at Weather Tree to discover that he, her adored father, hasn't opened her letters in six years. And then at the reading of the will, she learns that he has bequeathed her one dollar, leaving the rest to her cousin.

Abigail emerges from her shock determined to find out why he did this. She hires a private detective, an act that turns the novel into a detective-story quest. Why did her father disinherit his only child? Why, years ago, did he leave New York society to retreat to Weather Tree and become an alcoholic recluse? Moreover, should Abigail contest the will? And is she falling in love with the lawyer who helped him write it?

Great fun! Even the names of the characters are exhilarating, and of course Abigail's job and looks are glamorous, not to mention her clothes. But mention of her clothes is made often, for example, ''The stylish but casual lines of her jacket and pants made her look attractive, but Abigail was unaware of it.'' These too numerous references as well as shaky shifts in viewpoint are the main flaws that dull this glossy entertainment.

If the season were summer, ''Old Money'' could be called a beach book. At this time of year, it's a book to curl up with beside the fire, its description of luxurious, rich lives providing extra warmth.

Lacey Fosburgh has been a reporter for the New York Times, and her first book was nonfiction, ''Closing Time - The True Story of the Goodbar Murder.'' ''Old Money'' is her first novel.