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I lost your earrings you lent me. I try to buy another pair to compensate you.
... another ...
... a new pair ...

Hi,
Do all of the above sound right to you? Thanks.
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None of them do. Use these:

I lost the earrings you lent me. I'll try to buy another pair to replace them.
... a new pair ...
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Thanks, Mister.
But why doesn't "compensate you" work? Could you shed more light? Thanks.
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It is overly formal here; it would be used for something of greater value or importance.