Accelerating Charitable Efforts Act or the ACE Act This bill modifies tax rules relating to donor advised funds (DAFs) (separately identified funds maintained and operated by a tax-exempt charitable organization for which a donor retains advisory privileges with respect to the distribution of funds and the investment of assets). Specifically, the bill places certain restrictions on charitable contribution deductions for gifts made to a nonqualified DAF. It also sets forth rules for the treatment of private foundation administrative expenses paid to disqualified persons and for the treatment of distributions to DAFs from private foundations. The bill imposes a 50% penalty on contributions held in a DAF that are not timely distributed. The bill also sets forth special rules for the treatment of contributions from DAFs for purposes of meeting the public support test (the requirement that charitable organizations receive a certain percentage of their support from public sources). The bill exempts from the tax on the investment income of a private foundation (1) distributions to a DAF of not less than 7% of the foundation's assets, and (2) for foundations that have a duration, specified in their governing documents, of not more than 25 years.