The Love Tree – A Math Puzzler (?)

From Car Talk.

A teenage boy smitten with a teenage girl in his high school freshman class, made his feelings known. Overjoyed at finding them reciprocated, he took pen knife to a young hard wood in the vicinity and carved their initials within a heart, five feet up the tree’s trunk.

By their senior year, however, the girl’s ardor had cooled. She took her diploma, went away to the big city and married. The boy was crushed, inconsolable.

Bidding his family farewell, he took his small savings that he got from selling lemonade, bought a bus ticket, went to the east coast and shipped out in a menial job on a broken down freighter.

Twenty-five years later, captain of his own vessel, owner of a small freighter fleet and with a major interest in a few oil tankers, he indulged in a nostalgic whim and returned for the first time ever, to his old hometown.

Imagine his joy, when he discovered his old sweetheart living there, now a widow.
One thing led to another. The flame reignited, and one day they searched for their tree. It was not hard to find. It was near a rock, near a river, and they immediately found it.

Now, here’s the puzzler. If the tree had added 35% to its height in the first 15 years of his absence, 10% in the following in the five years and 2.5% in the ensuing eight years, how far up the trunk did they have to look to find the carving with their initials?

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