Use 'redound to' when discussing benefits stemming from actions or qualities. The team's effort will surely redound to our victory.
Pro Tip 2/3
Impersonal Subjects
'Redound to' is often used with impersonal subjects such as 'it' to discuss outcomes. It redounds to the company's credit that they've reduced emissions.
Pro Tip 3/3
Abstract Results
The phrase can refer to abstract results, not just concrete achievements. Her honesty will redound to her good reputation.