Police said they went to the address and arrested a 42-year-old suspect.
The holdup took place Tuesday at a Speedway station in the Grand Rapids suburb of Kentwood.
Police told The Grand Rapids Press the robber told the station clerk he had a gun. He appeared to be holding a weapon beneath a piece of paper.
After getting cash, the man dropped the paper and ran when the clerk made a move toward him.
Officers said the address on the paper was for a Grand Rapids apartment. They arrested the suspect when he arrived about an hour after the robbery.
The gun turned out to be a homemade fake.
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