Compound Interest Confusion

[firenv]

First time poster long time lurker. My husband and I are early 30's DINKS living in Nevada with relatively high incomes. After two years of diligently working to pay off student loans ($78,000) and several car and personal loans (~$25,000) we are finally non-mortgage debt free. We are fully maxing out our 401K's and hope to reach FIRE by mid-40's. My question is regarding compound interest and having multiple accounts (401K, Roth, and taxable accounts). I work for a company that allows me to put in an additional $25,000 a year in my after tax 401K for a total of $53,000 a year in mine/company investment. Is it smarter put the money that was going towards debt to into this account because of the power of compounding interest and then at FIRE do a backdoor Roth conversion or put all the extra money into a taxable account that we have access to at all times. I know this may seem a little vague but the main thing I am trying to understand is does compounding provide a larger return the more money in an account or is it the same no matter how many accounts you have with smaller balances?

[BarkyardBQ]

Whether you are compounding $1 in 5 accounts or $100k in 1 account, the compounding is the same for similar investments (fund class/asset class). It's important to consider the fees of each account and/or expense ratio of the funds in each account.

Most likely it's better to pay down your debts for any interest rate higher than 5 or 6%.

See the case study spreadsheet.

Are you in SONV?

[firenv]

Thanks that's what I thought but was confusing myself. We are in NoNV.

[Dezrah]

My understanding of the Mega Backdoor Roth (the extra $25k per year) is only worthwhile if you immediately roll it out of the 401k into an IRA. If you allow it to grow in the 401k you will owe taxes at your regular income (tax-deferred) on the earnings. If you roll it into a Roth IRA, the earnings are tax free.  If that same $25k were invested in a taxable account you would only owe capital gains on the earnings which is nearly always less than or equal to income taxes.

Plenty of people here are frugal an savvy enough to have an effective taxable income rate of 0% in RE, but unless you're sure of all your future incomes I'd take either the Roth rollover or just stick with taxable accounts.

[MDM]

I know this may seem a little vague but the main thing I am trying to understand is does compounding provide a larger return the more money in an account or is it the same no matter how many accounts you have with smaller balances?

Last question first: the compound interest equation is
FV = P * (1 + i)^n
FV = Future Value
P = Principal invested
i = annual interest rate
n = number of years

If you have accounts 1, 2, 3, etc.:
FV_1 = P_1 * (1 + i)^n
FV_2 = P_2 * (1 + i)^n
FV_3 = P_3 * (1 + i)^n
or...
(FV_1 + FV_2 + FV_3) = (PV_1 + PV_2 +PV_3) * (1 + i)^n
or...
Total Future Value = (Total Principal invested) * (1 + i)^n
...and it doesn't matter whether you had 3 smaller accounts or 1 big one - the results are identical (assuming each account earned the same interest rate).

...we are finally non-mortgage debt free.

Excellent!  That's probably ~4% or less on the mortgage?  As BackyarBQ implies, investing will likely (but not definitely) be better.  Here is the case study spreadsheet link - see the 'Investment Order' tab.

I work for a company that allows me to put in an additional $25,000 a year in my after tax 401K for a total of $53,000 a year in mine/company investment.
Is it smarter put the money that was going towards debt to into this account because of the power of compounding interest [you will pay less in taxes vs. investing in a taxable account] and then at FIRE [or earlier if your company allows in-service distributions] do a [mega] backdoor Roth conversion...?

Probably "yes" to the option as edited here.

See...
https://www.bogleheads.org/forum/viewtopic.php?f=2&t=137366
http://forum.mrmoneymustache.com/investor-alley/mega-backdoor-roth/
http://thefinancebuff.com/in-service-withdrawal-the-law-and-the-plan-rules.html
https://www.kitces.com/blog/irs-notice-2014-54-acquiesces-on-splitting-after-tax-401k-contributions-for-roth-conversion/
...for more on this.