Real Return After Tax

Three sliders: what the account pays, what prices do, what the tax office takes. The tax is charged on the whole nominal interest and nothing deducts the inflation first, so the share it takes of your real gain is larger than the rate written on the form, and how much larger depends on the account rather than on the tax code.

Worked example — Real Return After Tax

Real return after tax	+0.73%
Share of the real gain taken	62.5%
Cost of taxing the inflation	0.73%
Nominal rate to break even	4.00%
Worth in today's money at year 10	10,752.48

These are the values the calculator shows when the page opens. Change any input above to recompute them.

Loading interactive simulation...

A 25% tax that takes 62.5% of the gain 🖖

Press A taxed deposit. The account pays 5%, prices rise 3%, so the real gain is 1.94% a year: 1.05 divided by 1.03, less one. The tax office charges 25% on the 5%, not on the 1.94%, which leaves 3.75% nominal and 0.73% real. Tax has taken 1.21 of the 1.94 points, and without the rounding that share is exactly 62.5%. That is not an artefact of these three numbers. Both real returns carry the same 1/(1+i) and it cancels in the ratio, so what is left is exact rather than a small-rate approximation: the share taken is t·n/(n−i), here 0.25 × 5/2. Your statutory rate is multiplied by n/(n−i), the ratio of what the account pays to what it pays above inflation. Press The same tax, a higher rate and that multiplier falls to 12/9, so the same 25% now takes 33.3%. It works downward too: at 3% interest and 2% deflation the ratio drops below one and the same 25% takes 15%.

Between 3% and 4% you are taxed on a gain and end up poorer 🖖

Press Taxed on a gain, poorer anyway. The account pays 3.5% against 3% inflation, so before tax you are 0.49% ahead for the year. The tax office sees a 3.5% gain and takes a quarter of it. After tax the account pays 2.63% while prices rise 3%, and you finish the year 0.36% behind. The band where this happens has ends you can write down. It opens at n = i, where an untaxed saver breaks even, and closes at n = i/(1−t), which the tool prints as the break-even nominal rate: 3 divided by 0.75 is 4.00%. So the band is i·t/(1−t) wide, one point at 25% tax and three points at 50%. Drag the tax slider and watch the shaded strip stretch to the right while the green line does not move at all, because nothing about the pre-tax real return depends on the tax. Inside that strip the same year is a real gain before tax and a real loss after it.

The inflation part of the bill is the same at 1% interest and at 12% 🖖

Two presets differ in one slider. A taxed deposit pays 5%; The same tax, a higher rate pays 12%. Inflation is 3% and the tax is 25% on both. The real return jumps from 0.73% to 5.83%, the share of the real gain taken falls from 62.5% to 33.3%, and the third card does not move: 0.73 percentage points on both. That card holds the gap between the tax as it is levied and a tax charged on the real gain alone, and the gap works out at t·i/(1+i). The nominal rate is not in it. Whatever the account pays, taxing the inflation costs a 25% taxpayer 0.73 points of real return a year when prices rise 3%, and a 40% taxpayer 2.62 points when they rise 7%. On the chart it is the constant vertical distance between the amber line and the blue one. Those two are parallel because the tax rate alone sets the slope of both and only their intercepts differ, by exactly that t·i/(1+i). Martin Feldstein set the argument out for American savers in 1976: leave a tax code unindexed and inflation raises the real burden on savings without anyone voting for a rate change.

Problem solved in full

Real return on 10,000 in an account paying 5% a year 8 steps
You have 10,000 in an account paying 5% a year. Inflation is 3%. Tax takes 25% of the interest each year, as it is credited. What is the real return after tax, what share of the real gain has the tax taken, and at what tax rate would you be standing exactly still?
1. Start with the real return before any tax, and use Fisher exactly rather than subtracting 3 from 5. Your money grows by a factor of 1.05 while the things you buy cost 1.03 times as much.
  
  $r = \frac{1.05}{1.03} - 1 = 0.0194175 = 1.94175%$
2. The tax is charged on the interest the bank credits, which is the whole 5%. Nothing deducts the inflation first.
  
  $5% \times (1 - 0.25) = 3.75%$
3. Now deflate that smaller number the same way.
  
  $r_{a} = \frac{1.0375}{1.03} - 1 = 0.0072816 = 0.72816%$
4. Subtract, and take what the tax removed as a share of the gain there was to begin with.
  
  $\frac{1.94175 - 0.72816}{1.94175} = \frac{1.21359}{1.94175} = 0.625$
5. Do that division with letters instead of numbers. Both real returns are divided by 1 + i, so it cancels, and what is left is exact rather than an approximation that is good for small rates.
  
  $T_{eff} = \frac{r - r _{a}}{r} = \frac{t n / ( 1 + i )}{( n - i ) / ( 1 + i )} = \frac{t n}{n - i} = 0.25 \times \frac{5}{2} = 62.5%$
6. Now read the same identity the other way. The real return after tax is zero when the after-tax nominal rate lands exactly on inflation, so solve n(1−t) = i for t.
  
  $n (1 - t) = i ⟹ t^{*} = 1 - \frac{i}{n} = 1 - \frac{3}{5} = 40%$
7. Check both against the tool. It prints 0.73% and 62.5%, and a break-even nominal rate of 4.00%, which is the identity solved for n rather than for t. Drag the tax slider to 40% and the real return card reads +0.00%.
  
  $\frac{i}{1 - t} = \frac{3%}{0.75} = 4.00%$
8. One thing the tool holds fixed that a tax wrapper does not: when the tax is taken. Here it leaves every year, so it never compounds. Defer it instead, and tax the whole gain once at the same 25%: the ten years finish at 16,288.95 gross, 14,716.71 after tax, and 10,950.61 in today's money. Same rate, same account, 198.13 better off, entirely from the timing. That is the arithmetic behind every tax-deferred wrapper, and there is no slider for it above.
  
  $\frac{10 , 000 \times 1.0 5 ^{10} - 0.25 ( 6 , 288.95 )}{1.0 3 ^{10}} = \frac{14 , 716.71}{1.34392} = 10, 950.61$
Answer

0.73% a year in real terms, and the 25% tax has taken 62.5% of the real gain. At a tax rate of 40% you would stand exactly still. The amplification is t·n/(n−i), and the rate that wipes out the gain is 1 − i/n.

By the 42Math team · Updated 2026-08-26

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

A taxed deposit - 5% in the account, 3% inflation, 25% on the interest. The real return after tax is 0.73% a year, the tax has taken 62.5% of the real gain, and 10,000 left alone for ten years shows 14,450.44 on the statement while buying 10,752.48 of today's goods.
Taxed on a gain, poorer anyway - Half a point more interest, at 3.5%, and nothing else changed. Before tax the account is 0.49% ahead of inflation; after tax it is 0.36% behind. Ten years of that turns 10,000 into 12,957.81 on the statement and 9,641.83 in what it buys.
The same tax, a higher rate - The same 3% inflation and the same 25% tax, with the account paying 12% instead of 5%. The share of the real gain taken drops to 33.3%, the real return climbs to 5.83%, and the inflation surcharge card still reads 0.73%.
High inflation, high tax - 9% interest looks generous until prices rise 7% and 40% of the interest is taxed. The real return is −1.50% a year, you would need 11.67% just to stand still, and taxing the inflation alone costs 2.62 points a year. Ten years takes 10,000 down to 8,601.38 in today's money.