Company: MYI
Filing Date: 2025-07-15
Form Type: 425
Source: 0001193125-25-159406
Chunk: 5

Company: BLACKROCK MUNIYIELD QUALITY FUND III, INC.
Filing Date: 2025-07-15
Form: 425
Chunk 5
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 per Share was $7.21 and the last reported market price for a Share on the NYSE on                                                                                                                                          
 such date was $6.58, representing a discount to NAV of (8.74)%. The NAV on the Pricing Date may be higher or lower than the NAV as of July 8, 2025, and the discount to NAV at which the Shares trade may be greater or lesser than the discount as 
 of July 8, 2025. For the Fund’s most current NAV and market price per Share, you may view online at                                                                                                                                                 
 https://www.blackrock.com/us/individual/products/240201/blackrock-munivest-fund-inc-usd-fund. For additional questions or                                                                                                                           
 information during the pendency of this Offer, you may contact the Information Agent by calling (866) 961-8329, between the hours of 9:00 a.m. and 11:00 p.m., Eastern                                                                              
 time, Monday through Friday (except holidays), and 12:00 p.m. and 6:00 p.m., Eastern time, on Saturday. (See Section 10, “Price Range of Shares.”)                                                                                                  |

Will the Fund’s NAV per Share be higher or lower on the Pricing Date?

Does the Fund have the financial resources to pay me for my Shares?

| • |     | Yes. If the Fund purchased 1,433,392 Shares (2.5% of the Shares outstanding as of July 8, 2025) at a price                                                                                                                                               
 per share of $7.07, equal to 98% of the NAV as of July 8, 2025 ($7.21 per Share), the Fund’s total cost, not including fees and expenses incurred in connection with the Offer, would be approximately $10.1 million. The Fund intends to                
 first use cash on hand to pay for Shares tendered, and then intends to sell portfolio securities to raise any additional cash needed for the purchase of Shares. The Fund currently does not intend to borrow money to finance the purchase of Shares in 
 the Offer. (See Section 8, “Source and Amount of Consideration.”)                                                                                                                                                                                        |

How do I participate in the Offer?

| • |     | If your Shares are registered in the name of a Nominee, you should contact that firm if you wish to tender your 
 Shares.                                                                                                         |

| • |     | All other stockholders wishing to participate in the Offer must, prior