Which interest rate is better?

[Leeling Chew]

We were given these two options when we refinanced our house recently: 5.25% with $8000 cost OR 5.875%. My husband chose 5.875% with the following reasoning:
"If I had applied for a 5.25% rate for a $401250 loan, the loan would cost $8000 more and the payments would be $158 less per month. I applied for a 5.875% rate for a $401259 loan. i will take the $8000 extra, apply to the principal after closing. That will save $35k in amortized interest paid."
My 17 year old son, who has recently began to learn about real estate investing, didn't agree. His reasoning is as follows: 
"By paying $8000 toward the remaining principal, we would be left with $393,250. The interest isn't saved, it is merely avoided by borrowing less money on the first 19 amortized payments. Even if one considered the $8000 gone with closing costs for the 5.25% option, its $158 cheaper per month. Now that we are borrowing $393250 on both interest rates, we are just paying extra for 5.875%. If we were to refinance after 5 years, the amount saved in interest would total $9480(12*158*5), which is more than $8000."

We had spent several hours on this debate already. Who is right??

LL