1. What we know
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Main account annualized return (9 years): +23.59%
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Outperformance vs. QQQ (over 9 years): +$2.26M (≈ $251,208/yr)
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Outperformance vs. SPY (over 9 years): +$4.98M (≈ $553,353/yr)
So, after 9 years, the portfolio’s value is higher than if the same money had been invested in QQQ or SPY. That lets us back-solve the original investment (principal).
2. General formula
If
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PP = original principal,
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rr = annualized return (as decimal),
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nn = number of years,
then ending value is:
FV=P×(1+r)nFV = P \times (1+r)^n
We’re told the actual portfolio earned 23.59% CAGR for 9 years, so:
FVportfolio=P×(1.2359)9FV_{portfolio} = P \times (1.2359)^9
3. Relating to QQQ and SPY
We also know:
FVportfolio=FVQQQ+2.26MFV_{portfolio} = FV_{QQQ} + 2.26M FVportfolio=FVSPY+4.98MFV_{portfolio} = FV_{SPY} + 4.98M
where FVQQQ=P×(1+rQQQ)9FV_{QQQ} = P \times (1+r_{QQQ})^9.
Unfortunately, the statement didn’t give exact QQQ or SPY CAGR for the same 9-year period. But we can approximate from history:
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2015–2024 9-year CAGR (approx):
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QQQ: ~17%/yr
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SPY (S&P 500): ~12%/yr
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4. Solve with approximation
Let’s compute with these:
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Portfolio: (1.2359)9≈7.47(1.2359)^9 ≈ 7.47. So FVportfolio=7.47PFV_{portfolio} = 7.47P.
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QQQ: (1.17)9≈4.35(1.17)^9 ≈ 4.35. So FVQQQ=4.35PFV_{QQQ} = 4.35P.
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Difference: 7.47P−4.35P=3.12P7.47P - 4.35P = 3.12P.
We’re told this difference equals $2.26M. So:
3.12P=2.26M⇒P≈0.724M3.12P = 2.26M \quad \Rightarrow \quad P ≈ 0.724M
So the original investment was about $720K–$730K.
5. Cross-check with SPY
If SPY CAGR ≈ 12% → (1.12)9≈2.77(1.12)^9 ≈ 2.77. So:
7.47P−2.77P=4.70P7.47P - 2.77P = 4.70P
With P≈0.724MP ≈ 0.724M, difference = $3.40M, but reported difference = $4.98M.
This suggests my assumed SPY CAGR (12%) may be too low — the actual period return must have been a bit higher, otherwise the $4.98M gap wouldn’t line up. But the QQQ-based estimate is pretty consistent.
Conclusion
The original investment was about:
$700K–$750K (likely around $725K)\textbf{\$700K–\$750K (likely around \$725K)}
The exact number depends on the actual QQQ/SPY CAGRs over the 9-year period, but this is the right ballpark.
