Calculating the amount paid for a loan in today's dollars
The monthly payment formula tries to ensure that you pay a constant amount each month. Hence, in real terms, you are actually paying more up front as $117.46 today is worth more than in 20 years assuming positive inflation. The more you pay up front, the less you have to pay in total. Even if you managed to correctly calculate payments such that they were constant in real terms, you would end up paying more in nominal terms than if payments were constant in nominal terms.