A 23 year old maxing out his IRA and 401k has two options: Option A, to stay on his parent's health insurance for free and forgo the opportunity to invest in a health savings account (HSA) or Option B, to purchase health insurance from his employer for $X per year and become eligible to invest \$3500 of pre-tax money each year into an HSA, which grows and can be withdrawn tax free when used for qualifying medical purchases. He can stay on his parents' health insurance until he turns 27, at which point he must purchase insurance from his employer.
Assuming an annual effective income tax rate of 30% and an annual average stock market return of 7% (dividends reinvested), as well as a capital gains tax rate of 20%, at what is the maximum value of X for which the better option is to purchase health insurance from the employer? Assume the invested money will be withdrawn at age 62 in both cases and will be used for qualifying medical expenses.
I think I can quantify the future value of Option A as follows: $$\text{Option A}=(1-0.2)\times\sum_{n=0}^{3}X(1.07)^{39-n}=40.5773X$$ This would be the future value of the four years of after-tax money saved and invested in a taxable brokerage account (paying the 20% capital gains taxes). But I'm struggling to quantify the future value of Option B. It seems difficult because you have to consider that contributing the \$3500 reduces the taxable income and grows tax free, and the fact that it costs \$1500 each year.
My guess is this: $$\text{Option B}=(1-0.7\times0.8)\times\sum_{n=0}^{3}3500(1.07)^{39-n}=78111.3$$
(I'm taking $0.7\times0.8$ because only 30% of the value of the HSA is tax savings and the other 70% could have been invested in a taxable account and must pay the capital gains tax.)
I am not sure about this answer. In option A, I don't consider the opportunity cost of the tax savings and in Option B I don't consider the \$1500 price tag of the HSA, but I think they cancel out in the comparison. If my comparison is right, then $X=\$1925$. But there are a lot of details here and I'm not sure that I'm taking the opportunity costs into consideration properly.
Are my equations correct? What value of $X$ do you get?