This gives me a total interest paid (over 10 yrs) of $10,420 with monthly payments of $405. Now averaging the total interest accrued over the 10 yrs yields an annual interest paid of $1,042. Dividing that number by the original principal gives me:

Annual interest rate of 2.72%.

This means (to me at least) that, if I only made minimum payments on the loan, that my effective interest rate over the 10 yrs is only 2.72% (mainly because a part of the minimum payment goes toward the principal, so the interest accrued decreases over time). E.g, if I have $10,000 left, then a month of interest is 10,000 * 0.05 / 12 = $41. Then the min payment of $405 will have $360 go toward the principal, effectively paying down the loan without me having to spend extra cash toward the loan.

Therefore, as long as I make the minimum payment, there's no reason to spend any leftover cash to pay the loan off early as long as I can find an investment with a return of 2.72%. Am I wrong about that?

This gives me a total interest paid (over 10 yrs) of $10,420 with monthly payments of $405. Now averaging the total interest accrued over the 10 yrs yields an annual interest paid of $1,042. Dividing that number by the original principal gives me:

Annual interest rate of 2.72%.

This means (to me at least) that, if I only made minimum payments on the loan, that my effective interest rate over the 10 yrs is only 2.72% (mainly because a part of the minimum payment goes toward the principal, so the interest accrued decreases over time). E.g, if I have $10,000 left, then a month of interest is 10,000 * 0.05 / 12 = $41. Then the min payment of $405 will have $360 go toward the principal, effectively paying down the loan without me having to spend extra cash toward the loan.

Therefore, as long as I make the minimum payment, there's no reason to spend any leftover cash to pay the loan off early as long as I can find an investment with a return of 2.72%. Am I wrong about that?

Not sure how you are coming up with a minimum payment of $50. Like you said yourself, the monthly payment over 10 years should be 405. If you only paid $50 you would basically be going into negative amortization, and would never pay it off. Seems like you are calculating interest on interest. In the first year, interest of 5% of 38,000 is 1900, which equals at least 158 a month just to stay even on interest. If you only pay $50, NONE of that would go to principal. You would be falling behind and the loan would get bigger and bigger. If you have one of those loans that lets you pay less any given month in case you have some sort of emergency and are short that month, well when you do that it prolongs the term of the loan. You end up paying more interest by doing so.

I can't think of it right now but there's something wrong with the terms your using. You are use amortization to calculate the total interest but then use the interest in a calculation that mimics you gaining interest as an investment. Its kind of like a logic puzzle.

Anyways,
If you put an extra $500 into one of your payments to go toward principal, you would NOT be gaining 2.72% on that $500. You would be effectively paying off/gaining $500 x 5% x term length left.

You can use the bankrate mortgage calculator to show how it affects your interest and term length. (They work the same way but bankrate has the optional one time payment choice)

So, if you can find an investment gaining more than 5%, put your money in that.. if not, extra money goes towards your highest interest loans.

As an attending, you'll make too much but if your wondering if you should pay your loans during residency, I believe so especially if you have a spouse/family and are itemizing deductions more than the standard deduction.

I just realized that it probably has something to do with the fact that in one scenario. You are working with a LOAN, in which you pay interest and pay back money you never owned.

In the other scenario, you have money that you own, collecting interest. (Interest/Investment)

Plus realize secured vs unsecured debt and the ability to disburse that debt under different circumstances.

e.g. if you got sued, if you got divorced, if you wanted to quit tomorrow, if you wanted to take a pay cut, if you got fired, etc.

student loans are NOT the same as "regular" loans.

My point being if you owe $125k in studen loans at 4.6%, and $125k on your mortgage at 4.75%. All things being equal, you may want to pay down the student loans first....if you got divorced you could split the mortgage, but not med school debt.

I think that you have to have a risk mindset and put a price on the % and risk of different scenarios.