Refund to Rainy Day Savings Act This bill directs the Internal Revenue Service (IRS) to establish and implement the Refund to Rainy Day Savings program (i.e., a program to provide for unexpected expenses) to allow taxpayers to deposit 20% of their income tax refunds into the savings program. The bill sets forth rules for investments in and disbursement from the savings program. The bill also reauthorizes the Assets for Independence Act for FY2021-FY2025. The IRS may make grants to qualified entities to conduct AFI innovation projects. The bill directs the Department of Health and Human Services to establish a three-year matched savings account pilot program to encourage savings by participants in the savings program.