An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties?

If 532,475 warranties were given, it means that 532,475 warranties were sold. The gross profit should be, 532,475 * $830 = $441954250. But then, this would still be subtracted with 12% of the warranties since they gave it back to the customers. Hence,

Profit = $441954250 - 0.12 (532,475) ($225)

Profit = $427,577,425