$12,333.45 wouldn't begin to buy you admission to a top ranked prep school today, not without additional and considerable financial aid.
A comparison: This past academic year, Lake Forest Academy charged day students $43,150 (48% of students are day students); boarders paid $57,700. 33% of the student body receives some aid. Over $5.1.million was awarded in financial aid. (LFA has @$30 million endowment; 150 acre campus)
Moving up a notch, tuition at *St Paul's School, Concord NH, this past year was $58,155 plus fees & expenses bringing you to $61,960. 39% of the student body receives some aid -- the average needs-based grant is $55,520. The financial aid budget this year was $11,200,000. A child whose family's total domestic income was under $125,00 qualified for FULL financial aid. If family income was a bit higher - but still less than $250,00 - the family needed to pay no more than 10% of that income (up to $25,000 tops) to tuition costs. (SPS has a $602,000,000 endowment; 2000 acre campus)
In any case, I never trust attempts to convert dollars from the past to relative worth in today's world. I have never seen a conversion that didn't way undervalue the modern day equivalent.
*Robert Mueller is a St. Paul's School alumnus, by the way