Is my relative obligated to pay Zakat on investment certificates that generate money, knowing that she has not paid Zakat before and wishes to repent, but she is not convinced that the money generated by these certificates is usurious?

If a mukallaf (accountable person) has passed years without paying zakat, while the conditions for its obligation were met, then he is unanimously obligated to pay it for all those years. As for depositing money in investment certificates, please refer to Fatwa no. 1220.