For people who failed fifth grade math, nostr:nprofile1qqs8msutuusu385l6wpdzf2473d2zlh750yfayfseqwryr6mfazqvmgpr9mhxue69uhhqun9d45h2mfwwpexjmtpdshxuet59uq3gamnwvaz7tmjv4kxz7tpvfkx2tn0wfnj77mvtex has your back on this one.
TLDR: Final Answer
Given the assumptions (BTC growth 30–50%, 25% tax, 1% buy/sell fee, dollar inflation 5%), holding Bitcoin yields significantly more after one year:
Lower end (30% growth): $120.31
Upper end (50% growth): $134.56
Holding dollars: $95 (purchasing power)
So based on the math, Bitcoin is better under these specific assumptions.
Full text:
Alright, let’s break this down step-by-step and compare the two scenarios over a one-year period.
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**1. Define the problem**
We’re comparing:
- **Bitcoin (BTC)**
- Expected annual growth: 30–50% (I’ll calculate a range)
- Short-term capital gains tax: 25% (applied to the gain only when sold)
- Transaction fee to buy/sell: 1% of transaction value (so total round trip cost = ~2% of principal if we buy then sell after a year)
- **Dollars (USD)**
- Inflation: 5% loss in purchasing power per year (no tax on holding cash)
- No transaction fees
Initial savings: Let’s take **$100** for easy calculation.
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**2. Bitcoin case**
Start with $100.
**Step 1 – Buy BTC**
Pay 1% transaction fee:
Amount actually invested in Bitcoin = \( 100 \times (1 - 0.01) = 99 \) dollars worth of BTC.
**Step 2 – BTC grows over 1 year**
Growth rate scenarios:
- **Lower end (30% growth)**
Value after growth = \( 99 \times 1.30 = 128.70 \)
- **Upper end (50% growth)**
Value after growth = \( 99 \times 1.50 = 148.50 \)
**Step 3 – Sell BTC**
Pay 1% transaction fee on final amount:
Post-fee value = Value after growth \( \times (1 - 0.01) \)
Lower: \( 128.70 \times 0.99 = 127.413 \)
Upper: \( 148.50 \times 0.99 = 146.415 \)
**Step 4 – Pay capital gains tax**
Capital gain = Final after-sale-fee amount minus initial $100 basis? Wait — careful:
Actually, capital gain = sale proceeds before tax minus cost basis.
But cost basis = $99 (what we paid for BTC after the buy fee).
Sale proceeds before tax but after selling fee: we already computed above (127.413 and 146.415).
So gain = Post-sale-fee amount − cost basis.
Lower: \( 127.413 - 99 = 28.413 \) gain
Upper: \( 146.415 - 99 = 47.415 \) gain
Tax = 25% of gain:
Lower: \( 0.25 \times 28.413 \approx 7.10325 \)
Upper: \( 0.25 \times 47.415 \approx 11.85375 \)
After tax = Post-sale-fee amount − tax
Lower: \( 127.413 - 7.10325 = 120.30975 \)
Upper: \( 146.415 - 11.85375 = 134.56125 \)
So final after-tax amount in dollars:
- **BTC 30% growth case → ≈ $120.31**
- **BTC 50% growth case → ≈ $134.56**
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**3. Dollar case**
Start with $100.
Inflation 5%: purchasing power after 1 year = \( 100 \times (1 - 0.05) = 95 \) in today’s dollars.
No tax, no fees.
Final purchasing power = **$95**.
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**4. Compare**
BTC (30% growth): $120.31 vs USD: $95 → BTC better by $25.31
BTC (50% growth): $134.56 vs USD: $95 → BTC better by $39.56
Even in the lower growth scenario (30%), Bitcoin yields more after taxes and fees.
---
**5. Check if BTC could be worse**
We can solve for the break-even BTC growth rate:
Let r = growth rate before fees.
After buy fee: invest \( 99 \)
After growth: \( 99(1+r) \)
After sell fee: \( 99(1+r) \times 0.99 \)
Gain = \( 99(1+r)\times 0.99 - 99 \)
Tax = 0.25 × gain
After tax = \( 99(1+r)\times 0.99 - 0.25[99(1+r)\times 0.99 - 99] \)
We want this = $95 (dollar case after inflation).
Let \( A = 99(1+r)\times 0.99 = 98.01(1+r) \)
After tax = \( A - 0.25(A - 99) = 0.75A + 24.75 \)
Set equal to 95:
\( 0.75 \times 98.01(1+r) + 24.75 = 95 \)
\( 73.5075(1+r) + 24.75 = 95 \)
\( 73.5075(1+r) = 70.25 \)
\( 1+r = 70.25 / 73.5075 \approx 0.9556 \)
\( r \approx -0.0444 \)
So if Bitcoin **decreases** about 4.44% per year, it breaks even with holding dollars (which lose 5% purchasing power). Any positive return >0% in BTC before fees likely beats USD given these assumptions.
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**Final Answer**
Given the assumptions (BTC growth 30–50%, 25% tax, 1% buy/sell fee, dollar inflation 5%), **holding Bitcoin yields significantly more** after one year:
- Lower end (30% growth): $120.31
- Upper end (50% growth): $134.56
- Holding dollars: $95 (purchasing power)
So based on the math, Bitcoin is better under these specific assumptions.
\[
\boxed{Bitcoin}
\]