Is this how refinancing an auto loan work?

Factual Questions
1

Ok, I know the basics: That you find a lender to pay off your original loan at a lower rate so you save money on interest.

However, wouldn’t you be saving money by financing only the amount that had not yet been paid off vs. the entire orignal principle? Let’s assume that the interest rate remains the same.

For instance, your original loan was for $25k over 60 months at 6% annual, making your payments about $483.32 per month. Say you make those payments for two years (24 months) and then choose to refinance.

You want to stick to the five-year pay off period, so you refinance the remaining $13400.32 over 36 months at 6%, reducing your monthly payments to $407.66.

Now let’s assume that you’re able to refinance at a better rate:

You want to stick to the five-year pay off period, so you refinance the remaining $13400.32 over 36 months at 4%, reducing your monthly payments to $395.63.

So, if you refinance at a lower rate, you end up saving based on both the lower rate AND the smaller principle, right?

Am I right? Did I miss something?

2

You’re confused. If you make payments on a $25,000 loan for 24 months at 6%, your principal balance is not $13400.32 – it’s much higher, because a good portion of that payment has only been paying interest. Let’s see what Excel tells me: those 24 payments mean you’ve paid a total of 11599.68 – but $2486.90 of that is interest, meaning your principal reduction was only $9112.78, not $11599.68. Thus the amount you’d refinance would be $15887.22. And of course you’d end up with the exact same payment.

So, to make the refi work, you’d need a lower interest, or cash to buy-down the principal. Let’s say, then, that you rifi at 4%. Remember your new principal is the $15887.22 value. This drops your payment to $469.05, a difference of $14.27 per month. Seems pretty minor, but if you can look at the grand scheme of things, that’s still a $513.57 savings over the remaining life of the loan.