VATICAN CITY—Every year, Catholics around the world donate tens of millions of dollars to the pope. Bishops exhort the faithful to support the weak and suffering through the pope’s main charitable appeal, called Peter’s Pence.

What the church doesn’t advertise is that most of that collection, worth more than €50 million ($55 million) annually, goes toward plugging the hole in the Vatican’s own administrative budget, while as little as 10% is spent on charitable works, according to people familiar with the funds.

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