Refinance federal loans privately, or stay federal? (forgiveness-aware)

Should you refinance federal student loans with a private lender? A private refi usually offers a lower fixed rate but permanently forfeits federal protections — income-driven repayment, forgiveness, and PSLF. This runs the borrower's best federal option (reusing the student-loan comparison) and weighs its present value of payments against a private refi's, so the rate saving and the forgiveness given up sit on the same scale. It also reports the refi rate that would merely tie the plain standard federal plan (the pure-rate breakeven), and which federal balance would be forfeited. Deterministic; not lending, tax, or financial advice.