Wealth & retirement · super (composes 4 primitives)
Vehicle TCO master
Type the price, MPG, and your driving pattern. We chain finance interest, depreciation curve, fuel + insurance + maintenance schedules, and the opportunity cost of the down payment to compute the real cost per mile and 5-yr total cost.
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Inputs
Result
True cost per mile: $0.74 · 5-yr TCO: $44,579
Reasonable: Within typical $0.55–$0.85/mi range. The biggest TCO lever is keeping the car past the loan payoff — depreciation flattens after year 5.
- 1
Monthly payment
$571
$33,000 financed at 7.50% for 72 months
- 2
Total interest paid
$1,234
Over the life of the loan
- 3
Fuel cost / year
$1,521
12,000 mi ÷ 28 mpg × $3.55
- 4
Depreciation (5 yrs)
$20,225
Year 1: $8,360 (22%); years 2+: 12% of remaining
- 5
Residual value at year 5
$17,775
What you'd get back selling
- 6
Insurance (5 yrs)
$9,250
$1,850/yr held flat — actual premiums change with vehicle age + your record
- 7
Maintenance + repairs (5 yrs)
$4,250
Steady $850/yr — back-loaded if you keep past warranty
- 8
Opportunity cost of down payment
$2,013
$5,000 at 7.0% for 5 years would grow to $7,013
- 9
5-year TCO (net of residual)
$44,579
Down + finance + fuel + insurance + maintenance + opp cost − residual
- 10
True cost per mile
$0.74
$44,579 ÷ 60,000 mi
Assumptions & notes
- Depreciation curve is non-linear — most vehicles lose 50% in the first 5 years, then 8-10%/yr.
- Opportunity cost is computed only on the down payment for simplicity. A more rigorous model would also count the monthly-payment delta vs. a cheaper alternative.
- Insurance + maintenance held flat — in reality both rise as the vehicle ages. The model under-counts by ~5-10% on a 5-yr horizon.
10-year projection
Vehicle residual value
Multi-scenario comparison
What if — ±20% on one input
| Scenario | Purchase price (out-the-door) | Headline | Δ vs baseline | Magnitude |
|---|---|---|---|---|
| −20% (cautious) | $30,400 | True cost per mile: $0.67 · 5-yr TCO: $40,250 | $-131 | |
| Baseline | $38,000 | True cost per mile: $0.74 · 5-yr TCO: $44,579 | 0 | |
| +20% (aggressive) | $45,600 | True cost per mile: $0.82 · 5-yr TCO: $48,909 | +$131 |
Try the input with the highest sensitivity (above). The Δ column shows the dollar swing from a 20% move — that's how much room you have for a counter, raise, or hedge.
Goal seek
Solve for an input value
Pick the input you want to vary and the output you care about. We'll find the input value that gets you to the target. Bisection-based; converges in < 50 iterations.
Monte Carlo simulation
Distribution under input uncertainty (500 trials)
We perturb every numeric input with normal-distributed noise (10–25% sigma depending on input type) and run 500 compute trials. The output is a probability distribution, not a single number — closer to how finance actually works.
Most-leveraged inputs (sensitivity analysis)
Where to focus — what moves the answer most
Each input perturbed ±10%; measured impact on Monthly payment. Higher elasticity = bigger lever.
- 1
Purchase price (out-the-door)
Elasticity ↑ 1.15× — 10% change in this input increases Monthly payment by 11.5%.
- 2
Loan term (months)
Elasticity ↓ 0.80× — 10% change in this input decreases Monthly payment by 8.0%.
- 3
Loan APR (%)
Elasticity ↑ 0.21× — 10% change in this input increases Monthly payment by 2.1%.
- 4
Down payment
Elasticity ↓ 0.15× — 10% change in this input decreases Monthly payment by 1.5%.
ShowMath is the only calc site that surfaces this. Adjust the highest-leverage input first — that's where small moves create big results.
Chain payload (for the 3D constellation)
{
"slug": "vehicle-tco-master",
"depth": 1,
"primitives": [
"car-payment-calculator",
"fuel-cost-calculator",
"depreciation-calculator",
"insurance-cost-calculator"
],
"composes": [],
"chain": [
{
"key": "monthly_pmt",
"label": "Monthly payment",
"primitive": "car-payment-calculator",
"numeric": 570.5737057120349
},
{
"key": "total_interest",
"label": "Total interest paid",
"numeric": 1234.4223427220932
},
{
"key": "fuel_annual",
"label": "Fuel cost / year",
"primitive": "fuel-cost-calculator",
"numeric": 1521.4285714285713
},
{
"key": "depreciation",
"label": "Depreciation (5 yrs)",
"primitive": "depreciation-calculator",
"numeric": 20225.0295296
},
{
"key": "residual",
"label": "Residual value at year 5",
"numeric": 17774.9704704
},
{
"key": "insurance_total",
"label": "Insurance (5 yrs)",
"primitive": "insurance-cost-calculator",
"numeric": 9250
},
{
"key": "maintenance_total",
"label": "Maintenance + repairs (5 yrs)",
"numeric": 4250
},
{
"key": "opportunity_cost",
"label": "Opportunity cost of down payment",
"numeric": 2012.7586535000019
},
{
"key": "total_tco",
"label": "5-year TCO (net of residual)",
"numeric": 44579.35338296495
},
{
"key": "cost_per_mile",
"label": "True cost per mile",
"numeric": 0.7429892230494158
}
]
}The chain explained
Each step above corresponds to a primitive calculator. Click any to see the stand-alone version with its own explainer + sources.
- car payment calculatorshipping soon
- fuel cost calculatorshipping soon
- depreciation calculatorshipping soon
- insurance cost calculatorshipping soon
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