The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: thd7t on April 22, 2015, 11:50:01 AM

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?

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.

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

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.

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 aftertax income (taxed @ 25%)
Plan 1:
Convert cash to debt payoff. Invest income in 401k. 401k grows to $44,200 pretax. If withdrawn at 25% is worth $33,150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 longterm capital gains rate.

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 aftertax income (taxed @ 25%)
Plan 1:
Convert cash to debt payoff. Invest income in 401k. 401k grows to $44,200 pretax. 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 longterm 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.

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

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.