What Round-Up Saving Actually Accumulates: A Bound on Spare-Change Programmes Under Stated Card Spending

Programmes that round each card purchase up to the nearest dollar and sweep the difference into savings are sold as painless wealth-building. This paper bounds what they can deliver under stated spending assumptions — 68 card purchases a month with a median purchase of USD 24 — simulated over 20,000 months. Rounding to the nearest dollar yields a median of USD 33.86 a month, or USD 406.32 a year; rounding to the nearest five dollars yields USD 169.27 a month. Reaching a USD 1,000 emergency fund from round-ups alone takes 30 months at the one-dollar setting and 6 months at the five-dollar setting. The implied saving rate is 1.40% of card spending — useful as a starter mechanism, arithmetically incapable of being a savings plan. The study is simulated, not measured. SIMULATED, NOT MEASURED.