Simply presenting a calculator's answer presents a difficulty, in that we don't know what code is being used. If the calculation is being done client-side and you have enough tech savvy to see what the code is, that would help.
But the main issue is how this 30/10 year matter affects the answer. To simplify it a bit, the 2% origination fee translates to $10,000. That $10,000 is then spread out among the interest payments, and the effective interest rate is calculated according to how that $10,000 increases the total money paid, relative to the interest paid. The more interest is paid, the more the $10,000 gets "diluted"; if you were only paying $10,000 in interest, then a $10,000 origination fee would be a drastic increase in the money paid, and so the effective interest would be drastically increased. In $1,000,000 in interest were paid, then the $10,000 would be a tiny amount, relatively speaking, and so would not have a very large effect on the effective interest rate.
So how does the term length affect the interest paid? Well, a 10 year amortization period means that each payment is enough to not only pay the interest, but pay down the principle so that after 10 years, there is no more debt outstanding. A 30 year amortization period, on the other hand, means that the payments are enough to pay it off after 30 years. This means that the payments will be lower, and at each period in the next 10 years, the 30 year mortgage will have a higher outstanding balance than the 10 year one. After 10 years, the 10 year mortgage will be at zero, but the 30 year one will still have 20 years of payments left.
Since the 30 year one is consistently carrying a higher balance, the interest will be calculated on a higher amount, and so the dollar amount of the interest will be higher. Thus, the origination fee will be diluted over a larger amount of interest paid, and the effective interest rate will be lower.
