The moon is moving away from us by 3.78 cm (1.48 in) a year.
The moon is currently moving at a rate of 1.48 inches per year (3.78 centimetres) as of now. The rate at which our fingernails grow is roughly the same. If the moon continues to move away from us at its current trajectory, it will reach its maximum distance from us within about 15 billion years.