Tips for refinancing an auto loan.

Purchased a vehicle with little-to-no credit at ~18 months ago.

The original loan amount terms were $25,966 @ 6.4% for 72 months which is roughly $436 monthly.

Currently, the remaining balance is $20,445.21 with 54 months remaining.

My credit score(724(mint.com),746(Capital One's estimator)) has increased since the conception of the original loan.

If I could refinance with an loan whose interest rate is at least half of the current (or 3.2%) for a term of 60 months (extending the current loan by half a year), it should shave at least $60 from the monthly payment.

Wouldn't this also decrease the total cost of the loan as well?

Whereas the remaining principal of $20,544 @ 6.4% over 54 months would be ~$23.5k. $20,544 @ 3.2% over 60 months would be ~$22.1k.

Either way, I plan to pay either loan off well before it actually matures, I'm simply looking at opportunities to reduce the current monthly payment amount.