Assume you make 16k/yr for 45 yrs of your working life. You put $4k in an IRA each year with a 7% interest rate. You can also make 7% interest outside your IRA. Let's assume you live an extra 20 years after retirement and withdraw everything in your IRA to use for the remaining 20 years of your life. In this case, your IRA would contain roughly 1.22 million $ when you retire. Of this 180k is principle and 1.04 million is interest.
Scenario 1: You choose a Roth IRA, and pay $400/year in taxes while working. But in retirement, you pay zero tax. In this case, you paid a total of 18k in taxes.
Scenario 2: You invested in a regular IRA. Here you saved 18k in taxes over the 45 years of working due to deductions. And if you were continually reinvesting this income, at 7% interest rate (and but deducting the 15% tax the gov takes on interest income), you would turn the tax savings into 89k.
So which is better scenario 1 or scenario 2? Well, if you divided the 1.04 million interest income in your IRA by 20 (years of withdrawals), you get 52k in interest income / yr. Now subtract the standard deduction and you have 40k per year of taxable income. So you'd pay around 5k per year in taxes on that income. That is about 100k saved in taxes over the 20 years.
IRA: money saved 89k (investing saved taxes)
Roth IRA: money saved 100k (taxes you don't have to pay when you retire)
Roth wins in the above scenario. There are a ton of assumptions in this calculation to make the math easier, and I'm guessing you could construct scenarios where the regular IRA wins. One assumption is that interest making stops once you start retirement, another is that you only live 20 yrs past retirement. The 7% interest rate is also uncertain. I assumed the Roth IRA would be favored by a ton, but when doing the math it appears that both retirement options save you similar amounts of money.
One reason to choose the Roth is that tax rates are currently at historic lows. If they were to raise in the future, your interest income would be exempt from these raises, because you pay no taxes on interest income in a roth.