ou are buying a $$30,000$ car from your dealership. You are initially offered $12\%$ APR with $600$ FICO score for your $$30,000$ auto loan over $5-$year period. Your monthly payment is $$667\mathrm{.}33.$

Then, when you are trying to make your final contract to buy your car in your dealership. Senior manager comes to you and says that if you purchase $5-$year service warrant which costs you $$5,000,$ they will offer you $3\%$ APR for $5-$year loan period. Your monthly payment is $$628\mathrm{.}90.$

Should you accept this offer? If so$,$ why? If not, why?