Author Topic: Not this question again! Math help on paying low interest debt  (Read 2710 times)

thd7t

• Handlebar Stache
• Posts: 1340
Not this question again! Math help on paying low interest debt
« 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?

neo von retorch

• Magnum Stache
• Posts: 3623
• Location: SE PA
Re: Not this question again! Math help on paying low interest debt
« Reply #1 on: April 22, 2015, 11:52:33 AM »
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

• Senior Mustachian
• Posts: 10302
Re: Not this question again! Math help on paying low interest debt
« Reply #2 on: April 22, 2015, 11:53:25 AM »
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

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• Posts: 1340
Re: Not this question again! Math help on paying low interest debt
« Reply #3 on: April 22, 2015, 11:54:33 AM »
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

• Magnum Stache
• Posts: 3623
• Location: SE PA
Re: Not this question again! Math help on paying low interest debt
« Reply #4 on: April 22, 2015, 12:04:34 PM »
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

• Handlebar Stache
• Posts: 1340
Re: Not this question again! Math help on paying low interest debt
« Reply #5 on: April 22, 2015, 12:10:01 PM »
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

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• Posts: 3623
• Location: SE PA
Re: Not this question again! Math help on paying low interest debt
« Reply #6 on: April 22, 2015, 12:15:44 PM »
Only the growth would be taxed - \$2900 is 15% of the \$19,343. So \$36,440ish left over.

thd7t

• Handlebar Stache
• Posts: 1340
Re: Not this question again! Math help on paying low interest debt
« Reply #7 on: April 22, 2015, 12:22:14 PM »
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.