Subtracting inflation from your return is a shortcut that always flatters you. This is the exact real return, and what the balance is actually worth.
Exact real return = (1 + nominal) divided by (1 + inflation), minus 1, expressed as a percentage. The shortcut everyone uses is nominal minus inflation, which is only close when both rates are small: it works on differences while compounding works on factors. The gap widens as inflation rises, and it always runs the same way — the shortcut overstates. To restate money in today's prices, divide by (1 + inflation) raised to the number of years, which is also how the $100 figure here is produced: $100 of goods today against that same basket after the horizon.
At 7% nominal and 3% inflation over 20 years on $10,000, the exact real return is 3.88% a year while the shortcut says 4.00%, an overstatement of 0.12 points. Small as that looks, compounding it for two decades is the difference between two different endings. The account itself reads $38,697 in nominal dollars. Deflated back to today's prices that is $21,426, and $100 of today's purchasing power is worth only $55.37 by then. The distance between $38,697 and $21,426 is exactly what the subtraction shortcut hides.
One flat inflation rate held for decades is an assumption, not a forecast: US CPI has run below zero and above 8% within a single working lifetime. Your own basket inflates differently from the headline index — housing, healthcare and college tuition have historically run hotter than goods. Nothing here accounts for taxes, fund fees or withdrawals, all of which erode real wealth faster than inflation does, and it assumes a certain nominal return with no volatility, so it cannot describe sequence risk or the order in which good and bad years arrive.
This is arithmetic for planning. It predicts no return, guarantees no outcome and recommends no product. Do your own research and, where relevant, speak with a qualified adviser.