Opportunity cost: reduce your debt or follow your heart?

How does a gap year (between med school and residency) effect your ability to pay off your student loan? Does the delay in attending salary by one year make a financial difference? Let's walk through it.

Our case

The questioner wants to know if paying down one's loan is worth postponing an attending salary for one year. What we will do in this exposition is find the "indifference point" - the point at which the cost of one option is equal to the cost of the other.

Based on the cost at the indifferent point, you'll be able to determine which option would work best for you. First, let's set the stage: we will compare 2 pairs of scenarios. In each scenario, we will look at the costs associated with a public or private med school education.

Basic info

Let's look at the annual tuition for a medical school. According to @Forbes, the mean tuition in CY2022 for:

• public med school = $38,947

• private med school = $61,023

Tuition growth rate

Medical school is typically 4 years (I'm not considering an MD-PhD or MD-MBA joint program, or an accelerated program). Tuition increases at a growth rate of 3.5% per year (as per @SOFI)

Annual tuition growth rate

Let's account for the increase in tuition every year for 4 years at a 3.5% growth rate. That is shown in Lines 4-7. Now, the natural thing to do is add up Lines 4-7 and that would be how much you pay for a 4-year med school education (public or private).

Economic cost

To get the economic cost we must consider the time value of money. $1.00 @ t=0 ≠ $1.00 @ t=1 ≠ $1.00 @ t=2 ≠ $1.00 @ t=3. All these future cash flows need to be compounded forward to one point in time. We will choose t=3 which represents the 4th/final year of med school. To get the single compounded value at t=3 we need the cost of capital. According to @bankrate the stated annual interest rate for a school loan is 3.75%. Since the loan is compounded monthly, we have a discrepancy in unit of time (annual interest rate but monthly compounding).

Let's convert the stated annual interest rate to an effective monthly rate, then convert that to the effective annual rate. We will use the effective annual rate for all calculations moving forward.

Period 0 (line 4) is the first year of medical school.

Effective rate

Now that we have effective annual rate, we can calculate the single value of the loan amount at t=3 (the final year of a 4-year med school career). Lines 18-21 represent the value of the loan at t=3. These values CAN be arithmetically summed.

Line 22 is the single value of the cost of a 4-year med school education accounting for the opportunity cost of investing your money in a bank instead AND the time value of money.

• Public school: $173,515

• Private school: $271,868.

You can add present values (PVs) together, or future values (FVs) together, but you cannot add a PV and a FV together (even though you really want to).

Decision

The questioner has the option of taking a *gap year* and lowering the principal by $60,000. First, we need to compound the value in Line 22 one period forward. That's because you need the full year in period 4 to accumulate the $60,000 so that you can lower the principal.

In Scenario A and A', you have successfully reduced your remaining liability (Line 24). Observation: We have time asynchrony. If you selected Scenario A/A', you are 1 year behind in residency. Assumption: in any of the 4 scenarios, you make no payment during residency.

The questioner doesn't indicate which residency s/he selected. This fact matters a lot. For now, we will select the shortest residency: 3 years (Line 27).

For a 3-year residency, we must compound the remaining liability for 3 years at a cost of capital of 3.82% - the effective annual rate (Line 9). Values in Line 29 are those who went from med school directly into residency. Values in Line 30 are those who chose the gap year.

Hopefully you are able to pay down some of your principal during residency.

Lines 29 & 30 represent the remaining liability at the end of the 3-year residency. But, the periods are different. Those who chose Scenario A/A' (gap year) are in Period 8 of the compounding process. Scenario B/B' folks are in Period 7. Reminder: $1.00 @ t=7 ≠ $1.00 @ t=8.

The questioner wants to know if delaying 1-year of an attending salary is worth it. In other words, how much of the 1st-year of an attending salary must folks in Scenario B/B' pay to lower their remaining liability to an amount EQUAL to what folks in Scenario A/A' have.

Line 31 answers the above question for folks who chose Scenario B/B'. First, we compound their outstanding liability from Period 7 to Period 8 (Line 31). Second, we want to know the payment that reduces Line 31 for folks in Scenario B/B' to Line 30 for folks in Scenario A/A'.

That amount is Line 31. For those who chose to enter residency from med school (no gap year): • public school grad: would need to pay $74,822 to reach liability parity with his/her gap-year-choosing counterpart • private school grad: pay $79,180 to do the same above.

How much of Line 31 is your salary as a 1st-year attending? That will depend on your years in residency, residency type, etc. Since I'm a Nephrologist, I had to complete an IM residency. And the approx. 1st-year attending salary for a hospitalist is $200K (Line 32).

Sensitivity analysis

Is it worth taking a 1 year gap and reduce your loan by $60,000? Line 33 answers the question.

•Yes, if you can allocate < 37.41% of your 1st year attending salary to your principal payment

•No, if you can allocate > 37.41%

•Indifferent if you can allocate = 37.41%

Feel free to reach out to me if you'd like to perform a *sensitivity analysis* or have other questions.