As @adol16 stated, putting additional principal and paying off the loan early is good. But to understand how this all works, looking at it from a full payback period will help. A few things here. You cant't look at paying back large debt from the amount of the loan but rather as the percentage of your income. As you get further into practice, your income will go up, thus as a percent of the income, your student loan repayment will go down
Each year you get a new loan, and from the day the school disperses the money until deferment period end (6 months after graduation) you get simple daily interest applied. That is just amount of yearly interest broken down in daily amounts and added up. At the end of the 6 month deferment the interest is capitalized into a new principal (ie becomes the new total loan amount as you essentially borrowed the interest money you now owe). You will have multiple loan sources (stafford, gradplus, direct/private) and may have a few equations per year but I will give you an example with private loans with $45,000 ($45K) and 7% interest This assumes dispersing in September year 1 and you graduate June year 4 starting repayment September year 4. Hence I have 12 month loan increments (this is a 3 month deferment you can go to 6 months, just easier for this example calculation)
Example: $45,000 tuition difference per year borrowed at 7%
year 1 $45,000 + $13,600 (48 months interest) = $58,600 capitalized
year 2 $45,000 + $9,450 (36 months interest) = $54,450 capitalized
year 3 $45,000 + $6,300 (24 months interest) = $51,300 capitalized
year 4 $45,000 + $3,150 (12 months interest) = $48,150 capitalized
Total loans capitalization 3 months after graduation is $212,500
So total difference of the tuition would mean $212,500 when you graduate
But what does this mean? If you dont estimate or model what the conditions will be for paying it back, it just be an enormous number. Lets assume that you can pay interest only back while in residency. Lets assume conservatively that you are in primary care which has an current average salary of $195,000. Also remember that your salary will increase as your career goes on but the cost of what you borrowed remains the same. In essence, the cost of borrowing becomes a decreasing percentage of your income and thus becomes "cheaper" to payback as you move forward in time. Just to give example of what this would cost to pay back over 25 years at 7% interest would be $1,501.91 a month or just under $18,022.92 a year or 9% of a current primary care average salary. And that percent would decrease as your salary increase.
So is the difference worth 9% of your monthly salary? $18,000 a year?