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With cash-back: finance (price − rebate) at your bank's rate. With low APR: finance full price at the dealer rate. Compare total interest paid in each scenario. Cash-back is usually better at high dealer rates; low APR wins when the promotional rate is significantly below your bank's offer. Run both scenarios with your actual rate before visiting the dealership.
Very rough: compares annual cashback rewards to carrying a balance at two APRs plus a fee. Paying in full changes the tradeoff.
~Annual cashback value
$144
~Extra interest vs lower APR (on that balance)
$180
Net vs lower-APR card (after fee)
-$131