Cash vs Credit Calculator: Pay Now or Carry a Balance

The reward is $20. The interest is $72.89. Cash wins.

A 2% reward on a $1,000 purchase is $20.00 — free money, if you pay in full. Carry the balance for six months at 24.99% APR and the interest is $72.89 (exact $72.8875), so the card costs $1,052.89 against $1,000.00 in cash — CASH wins by $52.89. On the defaults — purchase $1,000.00, APR 24.99%, payoff 6 months, rewards 2.00% — the cash total is $1,000.00, the rewards are $20.00, the interest is $72.89, the credit total is $1,052.89, the monthly credit payment is $175.48, the interest as % of the purchase is 7.29%, the break-even payoff months are 0.9208, the break-even APR is 6.86% (exact 6.8571%), the break-even rewards rate is 7.29% (exact 7.2888%), and the 12-month lens is interest $135.36, credit $1,115.36 — CASH wins by $115.36.

At the defaults — purchase $1,000.00, APR 24.99%, payoff 6 months, rewards 2.00% — the cash total is $1,000.00, the rewards are $20.00, the interest is $72.89, the credit total is $1,052.89, CASH wins by $52.89; the monthly credit payment is $175.48; the interest as % of the purchase is 7.29%; the break-even payoff months are 0.9208; the break-even APR is 6.86% (exact 6.8571%); the break-even rewards rate is 7.29% (exact 7.2888%); the 12-month lens is interest $135.36, credit $1,115.36, CASH wins by $115.36. Check the identities: rewards = P × rewards rate; interest = m × P × (N+1)/2 with m = APR/12; credit = P − rewards + interest; winner = the lower total; monthly = credit ÷ N; interest % = interest ÷ P × 100; N_be = 2 × rewards ÷ m − 1; APR_be = 24 × rewards ÷ (N+1); rewards_be = m × (N+1)/2; 12-month interest = m × P × 13/2. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum.

The worked example, line by line

Setup: purchase $1,000.00, APR 24.99%, payoff 6 months, rewards 2.00%.

Line 1 — the cash total. Pay now: $1,000.00. No interest, no rewards.

Line 2 — the rewards. $1,000.00 × 2.00% = $20.00.

Line 3 — the interest. The monthly rate is 24.99% ÷ 12 = 2.0825% a month. With equal principal payments the balance falls from $1,000 to $0 over 6 months, so the interest is 2.0825% × $1,000 × (6+1)/2 = $72.89 (exact $72.8875).

Line 4 — the winner. Credit total = $1,000.00 − $20.00 + $72.89 = $1,052.89, so CASH wins by $52.89. The monthly credit payment is $1,052.89 ÷ 6 = $175.48.

Line 5 — the break-evens. The break-even payoff months are 2 × 0.02 ÷ 0.020825 − 1 = 0.9208 — any carried balance beyond the grace period loses money: at N = 2 the interest is $31.24 and CASH wins by $11.24. The break-even APR is 24 × 0.02 ÷ 7 = 6.86% (exact 6.8571%). The break-even rewards rate is 0.020825 × 3.5 = 7.29% (exact 7.2888%).

Reverse: the purchase price for a credit total of exactly $1,000 is $949.77 (exact $949.77); rewards $19.00, interest $69.23, credit $1,000.00. The APR where credit ties cash at N 6 is 6.86% (exact 6.8571%); at the displayed 6.86% the interest is $20.01 — credit total $1,000.01, one cent over — at the exact 6.8571% the interest is $20.00, the tie. The first month where cash wins by $100 or more is month 11 (cash wins by $104.95, interest $124.95); at month 10 cash wins by only $94.54. The rewards rate for credit to win is 7.29% (exact 7.2888%); at the displayed 7.29% the rewards are $72.90 and the credit total is $999.99 — CREDIT wins by $0.01 — at the exact 7.2888% the credit total is $1,000.00, the tie. The purchase price where cash wins by exactly $50 is $945.40 (exact $945.40); cash wins by $50.00. The APR where 12 months of interest is exactly $100 is 18.46% (exact 18.4615%); at the displayed 18.46% the interest is $99.99, at the exact 18.4615% it is $100.00.

Every branch, checked

Pay in full (N 1): Cash $1,000.00, rewards $20.00, interest $0.00, credit $980.00 — CREDIT wins by $20.00. Monthly $980.00. 12-month: interest $135.36, credit $1,115.36 — CASH wins by $115.36. Pay inside the grace period and the interest is $0.00 — the $20.00 in rewards is free money, so CREDIT wins by $20.00. This is the ONLY credit win at the default APR.

12 months: Cash $1,000.00, rewards $20.00, interest $135.36, credit $1,115.36 — CASH wins by $115.36. Monthly $92.95. 12-month: interest $135.36, credit $1,115.36 — CASH wins by $115.36. Stretch the payoff to a year and the interest grows to $135.36 (exact $135.3625), so CASH wins by $115.36 — the same numbers as the 12-month lens.

APR 15%: Cash $1,000.00, rewards $20.00, interest $43.75, credit $1,023.75 — CASH wins by $23.75. Monthly $170.63. 12-month: interest $81.25, credit $1,061.25 — CASH wins by $61.25. Even at 15% APR the interest is $43.75 — more than double the $20.00 reward — so CASH wins by $23.75.

APR 0% (intro offer): Cash $1,000.00, rewards $20.00, interest $0.00, credit $980.00 — CREDIT wins by $20.00. Monthly $163.33. 12-month: interest $0.00, credit $980.00 — CREDIT wins by $20.00. At 0% APR the interest is $0.00, so CREDIT wins by $20.00 — the same as paying in full.

Rewards 5%: Cash $1,000.00, rewards $50.00, interest $72.89, credit $1,022.89 — CASH wins by $22.89. Monthly $170.48. 12-month: interest $135.36, credit $1,085.36 — CASH wins by $85.36. A 5% reward is $50.00, but the interest is still $72.89, so CASH wins by $22.89. Even a generous reward cannot outrun 24.99% APR.

Purchase $500: Cash $500.00, rewards $10.00, interest $36.44, credit $526.44 — CASH wins by $26.44. Monthly $87.74. 12-month: interest $67.68, credit $557.68 — CASH wins by $57.68. Halve the purchase and everything halves: rewards $10.00, interest $36.44, credit $526.44 — CASH wins by $26.44.

Purchase $5,000: Cash $5,000.00, rewards $100.00, interest $364.44, credit $5,264.44 — CASH wins by $264.44. Monthly $877.41. 12-month: interest $676.81, credit $5,576.81 — CASH wins by $576.81. At $5,000 the interest is $364.44 against a $100.00 reward — CASH wins by $264.44.

What the defaults assume

The model assumes EQUAL monthly principal payments — pay 1/N of the balance each month — so the interest is m × P × (N+1)/2. Real minimum-payment schedules cost far more, because the balance falls slowly and interest compounds on what is left. It assumes the rewards are paid in full on the purchase and are worth their face value — a reward you never redeem is worth $0. It assumes the APR stays flat for the whole payoff and that N = 1 means paid in full inside the grace period. With a $0 purchase the rewards are $0.00, the interest is $0.00 and both totals are $0.00 — a TIE, since there is no purchase and no cost either way. With 0% rewards the credit total is $1,072.89 and CASH wins by $72.89. With N = 1 and APR 0% the credit total is $980.00 and CREDIT wins by $20.00 — the same as the N 1 branch, because the APR does not matter inside the grace period. A payoff of 0 months is a validation error at the calc level — you cannot pay off a purchase in zero months. Rounding convention: totals are computed from unrounded values, so rounded parts may differ by a cent from their rounded sum; the reverses are nearest-value solutions, and the exact unrounded figures ($949.77, 6.8571%, 7.2888%, $945.40, 18.4615%) are stated wherever the rounded figures appear.

Output · formula · meaning

Who uses this

• The shopper eyeing a $1,000 TV: they learn CASH wins by $52.89 — and they check the pay-in-full branch (CREDIT wins by $20.00) to see the one case where the card wins.
• The cardholder on a 0% intro offer: they learn CREDIT wins by $20.00 — and they check the 15% branch (CASH wins by $23.75) to see what happens when the intro rate ends.
• The rewards-chaser with a 5% card: they learn CASH wins by $22.89 — even 5% cannot outrun 24.99% APR — and they check the 7.29% reverse ($999.99) to see the rate that would tie.
• The planner stretching to 12 months: they learn the 12-month lens is CASH wins by $115.36 — and they check the month-11 reverse ($104.95) to see when cash first wins by $100.

Accuracy & limitations

The math is first-principles card arithmetic: rewards = P × rewards rate; interest = m × P × (N+1)/2 with m = APR/12; credit = P − rewards + interest; winner = the lower total; monthly = credit ÷ N; interest % = interest ÷ P × 100; N_be = 2 × rewards ÷ m − 1; APR_be = 24 × rewards ÷ (N+1); rewards_be = m × (N+1)/2; 12-month interest = m × P × 13/2. The 4-decimal exact is shown where the rounding matters: the interest is $72.8875 (shown as $72.89); the break-even APR is 6.8571% (shown as 6.86%) — at the displayed 6.86% the interest is $20.01 (one cent over the tie), at the exact 6.8571% it is $20.00. The break-even rewards rate is 7.2888% (shown as 7.29%) — at the displayed 7.29% the credit total is $999.99 (CREDIT wins by $0.01), at the exact 7.2888% it is $1,000.00. What the model cannot do is price a real minimum-payment schedule: it assumes equal principal payments, so a card paid at the minimum costs far more than the numbers here — and it assumes the APR stays flat and the rewards are worth face value. For paying the card off, see the credit card payoff calculator and the credit card minimum payment calculator; for the APR itself, see the APR to APY table; and for the debt load behind the purchase, see the debt ratio calculator. This is a calculator, not financial advice.