The Baxters are a typical happy American family trying to live on too little money. Mrs. Polly Baxter acquires two mysterious trees that got into a nursery shipment by mistake. Guess what: they turn out to be money trees! After initial problems, Polly decides to spend the money. But there's one logical consequence of money grown on trees that no one's considered.

Polly Baxter runs an efficient, happy household for her husband Philip and their children, Diane, Flip and Midge. The sole irritant to their suburban life is Phil's meager earnings, from which he is saving to open his own accounting practice. One morning, a five-dollar bill blows in through an open window, and although Phil thinks they should look for its owner, Polly insists that they use it to buy shoes for Midge. That night, as Phil chastises his wife for spending ten dollars on two new trees, they realize that the cat is playing with a ten-dollar bill. Polly believes that the money, which they need to pay for home repairs, came to them because they needed it. The next day, however, when they find young Midge playing with thirty-five dollars she found outside, Phil insists on turning it in to the police, even though Diane needs a dress for her college dance. The police arrive a few days later to inform Phil that Polly has claimed the money as her own, and he yells at her. As she cries that they cannot afford to pay for Midge's tonsillectomy, they notice five- and ten-dollar bills floating around the lawn. While Phil calls the airport, thinking a plane may have dropped the money, Polly notices more bills on her new trees and, pulling apart the tree's buds, finds money in each one. Afraid to tell Phil, she covertly questions him on whether money grown on trees is legal, and he tells her to ask the Secretary of the Treasury. When the treasurer's assistant, Finlay Murchison, receives her letter, he, Internal Revenue Service executive John Letherby and Secretary of Agriculture Henry Carrollman compose a joking reply that she is welcome to use the money if it complies with all legal standards. Thrilled by the letter, Polly proceeds to secretly hoard cash. When Diane becomes engaged to bank teller Ralph Bower at the same time that Phil announces he has a one-month business trip, Polly plans a lavish wedding. She renovates the house and pays off the mortgage while Phil is away, attracting the notice of her dishonest neighbor, Mrs. Pryor, who sneaks into the Baxter kitchen one day. There, she finds and steals all the money, moving the letter from the Treasury into the wrong hiding spot. Phil returns from his business trip with the news that he was jailed for passing counterfeit money, which crumbled like dry leaves when he tried to pay for dinner. Soon after, Ralph, who took Polly's mortgage payment at the bank, is demoted when he refuses to inform the manager who paid a mortgage with bills that are now drying up and falling apart. That night, Diane hysterically informs Phil that Ralph accused Polly of counterfeiting, and Polly is forced to admit where the money came from. When she brings Phil outside, however, the trees are stripped bare, and she cannot find the cash or the letter. Phil thinks she is losing her mind. The policemen also question her sanity after Ralph is jailed and Polly tries to get him out. A newspaperman named McGuire overhears her story, however, and, after inadvertently discovering the Treasury letter in her coffee canister, immediately phones in the story of how the government sanctioned the use of home-grown money. Soon, the story spreads and the Baxter home overflows with curious tourists. Murchison, Letherby and Carrollman arrive with a horticulturist, Dr. Burroughs, but when they realize the tree has gone dormant for the winter, the officials demand that Polly retract her story, which will make her a felon. Just then, Burroughs announces that the tree has a bud, and for days the nation waits while it grows. A cold snap almost kills the bud, but Burroughs nurses it along until it yields a tiny ten-dollar bill. After Congress erupts, the government officials pay Polly for her trees, which die anyway because of the cold. Polly insists that the world is full of wonder if people would only believe in it, but a relieved Phil tells her wonder does not mix with real life. He goes off to work as Polly receives her newest bargain, a lamp which, when rubbed, begins to emit a curious smoke that signals a genie inside.