Not this question again! Math help on paying low interest debt

[thd7t]

Please help me with a bit of math.  It seems to be common wisdom, here that if one can invest money at a higher rate, that is a better idea than paying off debt.  I keep running into an issue with this, but I believe that there are some factors that I’m missing.  I will lay this out with rough numbers, here:

Generic debt: $20k @ 3.5% for 10 years
Payment: $200/month made after tax (really $197, but keeping it simple)

If one has $20k in cash, I would usually say that the thing to do is to invest this in an index fund and get the average 7% returns.  Over the course of the 10 years, one can hope to have about $40k. 
However, if one were to pay the debt in one stroke and then invest the initial payment in a pretax account (assuming 25% tax rate total) They’d be investing about $250/month for 10 years.  This, compounded over 10 years would yield about $43k.

Again, I have used some very generic numbers, here.  25% tax off of a paycheck (i.e. gross pay of $100 gives $80 in paycheck).  20k debt.  This really makes it look like leveraging this low interest debt is the wrong play.  What am I looking at wrong, here?

[neo von retorch]

How is it that the payment is $200/month but you're able to invest $250/month? If that's the case then add investing $50/month for 10 years to your example of not paying off the debt.

[MDM]

Seems you are comparing (or at least conflating) taxable vs. tax-advantaged.  That's not the same as comparing invest vs. pay debt - or am I misreading?

[thd7t]

How is it that the payment is $200/month but you're able to invest $250/month? If that's the case then add investing $50/month for 10 years to your example of not paying off the debt.

As I mentioned in the post, the debt is paid after tax, but the investment would be in a tax advantaged account.  401k, for example.

[neo von retorch]

Your arrangement is confusing, for sure.

Assets:
 $20k cash

Liabilities:
 $20k debt @ 3.5%; $200 payment

Income:
 $266.67 per month put in 401k
 - OR -
 $200 after-tax income (taxed @ 25%)

Plan 1:
 Convert cash to debt pay-off. Invest income in 401k. 401k grows to $44,200 pre-tax. If withdrawn at 25% is worth $33,150

Plan 2:
 Leave debt, invest $20k in taxable. Use taxed income to pay off debt, including $3700 in interest. $20k grows to $39,343.03; growth may be taxable at long-term capital gains rate.

[thd7t]

Your arrangement is confusing, for sure.

Assets:
 $20k cash

Liabilities:
 $20k debt @ 3.5%; $200 payment

Income:
 $266.67 per month put in 401k
 - OR -
 $200 after-tax income (taxed @ 25%)

Plan 1:
 Convert cash to debt pay-off. Invest income in 401k. 401k grows to $44,200 pre-tax. If withdrawn at 25% is worth $33,150

Plan 2:
 Leave debt, invest $20k in taxable. Use taxed income to pay off debt, including $3700 in interest. $20k grows to $39,343.03; growth may be taxable at long-term capital gains rate.

Withdrawn at 25% is a pretty big assumption, but sticking with it, the $39,343.03 would be taxed at 15% and be worth $33,441.  However, if retirement income is in the 15% bracket, both of those go up (cap gains go to 0%?).  It's very close.

[neo von retorch]

Only the growth would be taxed - $2900 is 15% of the $19,343. So $36,440ish left over.

[thd7t]

Only the growth would be taxed - $2900 is 15% of the $19,343. So $36,440ish left over.

Aha!  I missed that!  Thanks.  Mostly, I was trying to test "common wisdom".  Which is why I used a debt interest rate that is half of the ROI for investment.  I expected a bigger difference, though.  10% more is good, but there are two kinds of risk involved as expenses are higher while paying the debt and returns are not certain over such a brief timeline.

Again, thanks for the help.  Very clear.