Short answer: The working rule: if a single repair costs more than half of what the car is worth, or repairs are clustering month after month, replace it. Below that line, on an otherwise sound car, fixing it is almost always cheaper than a new loan.
Situation
Cost vs value
Do
One-off repair
< 50% of value
fix it
Big single repair
> 50% of value
price a replacement
Repairs clustering
any
replace
Start with the car's actual market value, then compare the repair against it. A $1,500 transmission on a $2,000 car is a replace; the same repair on an $8,000 car is an easy fix. Reliability history matters too — one big bill on a car that's otherwise been solid is different from the third surprise this year.
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Don't forget the hidden costs of replacing: sales tax, a new loan, and higher insurance on a newer car. A paid-off vehicle with modest repairs is often the cheapest thing in your driveway — right up until it isn't.