IRR vs CAGR — the real return when you contribute monthly

Say you put in $1,000 a month for 5 years. The result screen shows "$72,000 after 5 years" up top, and below it, the result cards display two annual return numbers. In gray: "Annual return (simple conversion)." In blue: "IRR (actual return)." Same outcome, two numbers. Why? Here's a walk through what they actually mean.

---

When you see two lines, when only one

When you run a DCA backtest (monthly contributions), the result cards show both lines. Run lump sum (one upfront purchase), and only one line shows.

The reason both appear in DCA mode is straightforward. The two numbers convert the same outcome two different ways. The final value of $72,000 is one fact. "What annual rate did the money have to grow at to reach that?" can be answered two ways.

• Gray line: simple conversion — calculated as if the entire contribution went in on day one
• Blue line: IRR — accounts for the fact that each monthly contribution went in on a different date

The two methods translate the same outcome differently. That's why the numbers usually diverge a bit. Gray reads 6.2%, blue reads 8.4%, that kind of thing.

The reason a small caption next to the gray card reads "may differ from IRR (actual return)." The two numbers aren't an error. The same result, two methods.

---

Where CAGR misleads in DCA

The gray line (simple conversion) calculates this way. Take the final $72,000, divide by total contributions of $60,000 — "the money grew 1.2x over 5 years." Then unwind that into 5-year compounding. The formula is (72,000 / 60,000) to the 1/5 power minus 1, giving roughly 3.7% annually.

The flaw is that it ignores when each contribution landed. The $1,000 in month 1 sat in the market for the full 5 years. The $1,000 in month 60 sat there for one month. Those two contributions had completely different time in the market — but simple conversion treats all 60 contributions as if $60,000 went in upfront.

That assumption tilts one way. Picture a case where the market rose strongly in the back half.

• Market rose strongly in the back half → late contributions also rose, so the result improves. But simple conversion assumes those late contributions were in from day one, so it underestimates the pace.
• Market rose strongly in the early half → early contributions caught the climb, late ones didn't. Simple conversion assumes everything caught it, so it overestimates the pace.

Simple conversion can't accurately capture the pace of a DCA result. It works for lump sum, but for DCA it's an approximation that ignores the timing.

That's why the simple-conversion card is toned down in gray — a visual signal that says "this is for reference, the real number is elsewhere."

---

Why IRR is the real number

The blue line (IRR) solves the timing problem precisely. It accounts for the fact that each $1,000 entered the market at a different date.

The method works like this. Tag each of the 60 contributions with "how many years did this one spend in the market?" Month 1's $1,000 carries a 5-year tag, month 2 carries 4 years 11 months, … month 60 carries 1 month. Combine all 60 tags and solve backward — what average annual rate would produce a final $72,000.

Solving that by hand doesn't work in one shot. Each of the 60 tags spent a different amount of time in the market. So a computer tries a number, checks the result, adjusts, tries again — narrowing the answer like balancing a bicycle. Usually a few dozen iterations reach a precise number.

This method captures the true pace of a DCA investment.

• Whether the market rose late or early, each $1,000's actual time in market is reflected
• Two $72,000 outcomes from different timing distributions land at different IRR figures
• It doesn't tilt the way simple conversion does

That's why the IRR card sits in blue. If gray is reference, blue is the real number.

---

Why the card colors differ

The UI color isn't decoration — it's a weight cue. Result cards split into two colors.

• Gray: simple conversion. "This is an approximation."
• Blue: IRR, cumulative return, and other key metrics. "This is the real number."

Same card design. Different colors. The reader's mental weighting splits automatically. Gray glances and moves on. Blue stops and reads. The color sets the hierarchy in advance.

A separate blue callout box below the result cards reads "IRR XX% vs simple conversion YY% (difference ZZ%)," restating the gap between the two numbers. The closing sentence carries the point.

For DCA investing, IRR is the recommended figure for actual performance.

Don't decide "my return is X%" from the gray card. Read the blue one next to it. The color and the callout box together signal which number is the real one.

---

One checkpoint when reading outside materials

Investment materials often state "X% per year" as a single number. One quick check worth running.

Is that "X% per year" simple conversion (CAGR), or IRR (actual return)?

For lump sum, the two are the same — either works. For DCA, pension contributions, or anything with recurring deposits, the two diverge. Some materials don't state which method they used, and some report simple conversion only.

Two quick filters.

• "IRR" appears in the text → actual return (time-weighted). The real number for DCA.
• Only "CAGR / annual return / simple conversion" appears → lump-sum framing. If the material covers DCA, treat it as an approximation.

The same "X% per year" carries different meaning depending on the method. Holding both concepts at once gives you an automatic verification step when reading outside materials.

That's part of why both numbers appear on the result card. Showing one alone makes it easy to lose track of which method produced it. Showing two together turns the gap itself into meaning.

---

Why IRR disappears in lump-sum mode

Run lump sum and the gray line disappears — only the blue line remains. "Annual return (CAGR)." Why?

Lump sum is the case where all the principal entered on the same day. With no timing differences, the tension between "simple conversion" and "IRR" disappears. The two calculations produce mathematically identical results.

• DCA: 60 entries across 60 different dates → timing correction needed → IRR calculated separately
• Lump sum: 1 entry on 1 date → no timing correction → CAGR equals IRR

That's why the IRR card doesn't appear in lump-sum results. No reason to display it. Same number written twice would clutter the screen.

Once you grasp the mechanism, reading other people's backtest results becomes easier. "This one's DCA, so IRR is the real number." / "This one's lump sum, so CAGR is the real number." The classification happens automatically.

---

Looking at it directly

Running it directly is the fastest way. Run a 5-year DCA simulation and read the gray and blue lines together. The moment you separate the two, "X% per year" stops sounding like one thing.

---

• This information is not investment advice.
• Past performance does not guarantee future results.
• Backtest results are simulations and may differ from actual trading outcomes.