Exhibit (a)(1)(iii)

Form of Letter from the Fund to Shareholders

in Connection with the Fund’s Acceptance of Shares

BLACKROCK PRIVATE INVESTMENTS FUND

c/o State Street Bank

Attn: Quincy Nunnally-Transfer Agency

1776 Heritage Drive

JAB/3

North Quincy, MA 02171

THIS LETTER IS BEING SENT TO YOU BECAUSE YOU TENDERED COMMON SHARES OF

BENEFICIAL INTEREST IN THE FUND, OR A PORTION THEREOF.

[Date]

Dear Shareholder:

BlackRock Private Investments Fund (the “Fund”) has received and accepted for repurchase (subject to any proration in the event the tender offer was oversubscribed) your tender of common shares of beneficial interest (“Shares”), or portion thereof, in the Fund.

In accordance with the terms of the tender offer, you will be issued a non-interest bearing, non-transferrable promissory note (the “Note”), which will be held on your behalf by State Street Bank and Trust Company, the Fund’s transfer agent (“Transfer Agent”), entitling you to receive payment(s) for your tendered and repurchased Shares (subject to any proration in the event the tender offer was oversubscribed) based on the estimated unaudited net asset value of such Shares as of September 30, 2024 (the “Valuation Date”), less the 2% “early repurchase fee” (if applicable).

Payment in respect of your Shares accepted for repurchase is expected to be made in two installments: an “Initial Payment” equal to approximately 90% of the estimated unaudited net asset value of the repurchased Shares determined as of the Valuation Date, and a “Contingent Payment.”

Your Initial Payment will be deposited into your account of record, or wired to the account that you designated in your Letter of Transmittal, no later than November 14, 2024, unless the Valuation Date has changed. Your Contingent Payment will generally be paid to you within 90 days of the Valuation Date. You will remain a shareholder of the Fund with respect to any Shares of the Fund that you did not tender (and, in the event the tender offer was oversubscribed, with respect to the portion of your Shares that are not repurchased by the Fund).

Your Contingent Payment is expected to be in an amount equal to the excess of (a) the net asset value of the Shares tendered and purchased as of the Valuation Date (as may or may not be adjusted based upon any corrections to the Fund’s net asset value as of the Valuation Date) over (b) the Initial Payment.

Notwithstanding the foregoing, if you tendered only a portion, but not all, of your Shares, payment in respect of your Shares accepted for repurchase is expected to be made, in full, in a single installment within 45 days after the Valuation Date, as described in the offer to purchase for the tender offer.

If you have any questions, please contact the Fund’s Transfer Agent at (888) 204-3956. Investors who invested in the Fund through a financial intermediary should contact their financial intermediary directly.

Sincerely,

BlackRock Private Investments Fund