If someone says that the six month interest rate is 5% quoted for an act/360 daycount with semi annual compounding, this means that the amount to pay on a loan of $1 to be repaid in a year is 1.025^2, right?
Well it depends on the frequency of the payment. It's unusual to quote a rate for a period shorter than the payment frequency, so most likely the loan has 2 payments (based on "semi-annual compounding") and each payment will charge interest of 2.5% of the remaining balance. If the payments were equal, then the loan would have to be amortized which is a more complex equation.
But that may have confused you even more... the basic idea is that the rate is divided by the compounding frequency.
Interest rates are typically annualized, meaning the periodic rate is multiplied by whatever number would represent a year's worth of periods. So for a semi-annual payment, the actual periodic rate would be multiplied by 2 to get the interest rate. Other terms, like APR, are annualized by applying the appropriate compounding, so if it said the APR was 5%, then the periodic rate would be
1.05^(1/2) -1 = 2.47%
Why don't they say things like "the six month IR is 5% PER YEAR" in order to make things unambiguous?
Rates that are not annual should explicitly say so (e.g. 0.5% per month) Even saying "5% per year" is ambiguous since you don't know if that 5% is a simple annualization or compound as described above. This is why "Interest Rate" and "APR" are industry standard terms that should have consistent interpretation.
Why is finance always worded in the most toxically vague way?
Mostly to keep things consice. If every car ad detailed the exact terms of a payment in the large print people would be much more confused. The actual terms are in the finds print that no one reads.
If something is vague to you, ask for clarification or go to the source to see what the actual terms are. The terms and conditions of any financial product will be much more explicit about the interpretation of the rates since they need to hold up in court in the event of a lawsuit.
To the vast majority of consumers, though, these differences are inconsequential. It may mean the difference between paying $500 a month for a car loan versus $502 per month.