Best no-penalty CD rates for June 2021 Bankrate 1 hr ago CDs usually have one characteristic that people don't like: penalties. Popular Searches Best no-penalty CD rates for June 2021 1. Ally Bank: 0.50% APY, $0 minimum deposit Ally is an online bank that was formed out of the GMAC Bank. Ally offers an 11-month no-penalty CD with no minimum opening deposit ($0.01). Ally also offers a Raise Your Rate CD in terms of two years and four years, as well as standard CDs in different terms. Term 11-month 2. Marcus by Goldman Sachs: up to 0.45% APY, $500 minimum deposit Marcus by Goldman Sachs offers three terms of no-penalty CDs: seven months, 11 months and 13 months.