A financially-strapped family of three was discovered dead early yesterday morning inside their burning Queens apartment in what appeared to be a murder-suicide, police said.

The family was discovered when firefighters responded to battle a pre-dawn blaze in their apartment on Roosevelt Avenue in Flushing.

The three — identified as Jong Lee, 50, his wife, Sung Lee, 54 and their son, Brian Lee, 15, — had slash wounds to their necks, police said.

Investigators believe the husband was distraught over a failed deal to finance a car and that the family was several months behind on paying the rent, said a law enforcement official.

Investigators found a note the husband wrote saying he didn’t want to die alone because it would cause too many problems for his family, a law enforcement official said.

He mentioned his financial problems, but didn’t go into detail, according to the official.

The husband appeared to have killed his wife and son in a bedroom of the sixth floor apartment, the official said, before dragging them into the living room.

The flames, which broke out just before 5 a.m., were contained to the living room of the apartment.

Their bodies were found in proximity to one another, the official said.

Investigators found the note inside the apartment, police said.

Jung Cho, 67, who had attended church with the family, said “we are all shocked, really. You’d never guess.”

Three firefighters were treated for minor injuries sustained while fighting the blaze, according to an FDNY spokesman.

(With anthony m. destefano)