FIN310 • Course Hub Fall 2026

This worked example starts at age 22 and ends at 62: 40 years, or 480 monthly deposits. The first monthly deposit is $1,000; deposits rise 5% each year. The baseline uses 2.5% annual inflation, a 0.10% annual fee, equal deposits, and a 20% effective tax on pre-tax withdrawals. A 22% current tax rate is used only for the equal-take-home-cost comparison.

These are selected classroom inputs, not current yields or forecasts. All returns include reinvested income before the modeled fee. This savings example does not enforce account contribution limits or eligibility.

The TIPS input is a real return. The other return inputs are nominal. Volatility approximates the standard deviation of annual log returns; it is not a maximum loss.

The annual 5% increase applies to the deposit, not a guaranteed salary raise or investment return.

Total deposits are not the final investment balance. Gains or losses are added by the investment model. All 16 choices use the same baseline savings habit.

Deposits arrive at the end of each month. Money already invested experiences that month’s return first; then the new deposit is added.

For a simple arithmetic demonstration only, suppose an investment earned exactly 8% every year with no fee or volatility. Its equivalent monthly growth factor would be 1.08^(1/12) ≈ 1.006434.

The actual calculator does not assume a fixed monthly return. It draws a different modeled return each month and includes the fee, as explained in step 10.

Portfolio weights specify how much of each investment the group chooses. For example:

The selected expected returns combine by weight:

Volatility is not simply the weighted average of the two volatilities. It also depends on how the investments move together.

These correlations are teaching assumptions, not claims about future markets. Portfolio weights are held constant by the model; it does not simulate an actual trading or rebalancing schedule.

For each investment choice, the app simulates 3,000 complete 40-year paths, sorts the ending balances, and finds the 10th, 50th, and 90th percentiles.

• Lower: 10th percentile of the simulated ending balances.
• Median: 50th percentile; the middle of those ending balances.
• Higher: 90th percentile.

The app interpolates between neighboring sorted values when needed. These are not three guaranteed market scenarios, ten-year periods, or worst/best cases. Outcomes below the lower and above the higher value can occur.

There is no single fixed-interest formula that reproduces a simulated median for a volatile investment. The value comes from the distribution of the modeled paths.

Fixed baseline: 2.5% annual inflation for 40 years; 0.10% annual fee; qualified Roth treatment; the deposits and return/risk inputs in steps 1–2. This table is a reference example and stays fixed while you change the calculator. Amounts are rounded from the unrounded simulation results.

Future balances are nominal dollars at age 62. Buying power is measured in starting-year dollars. A larger median alone does not make an investment the right choice for every saver.

To translate a future balance into starting-year purchasing power, divide it by the cumulative price-level increase.

Use the same balanced 60/40 median to isolate inflation’s effect:

The 60/40 nominal balance stays the same here because this calculator holds nominal return inputs fixed when inflation changes. It isolates the purchasing-power effect. It does not forecast how inflation might change company earnings, interest rates, valuations, or asset prices. TIPS are the modeled exception: their nominal return changes with inflation.

Roth and pre-tax describe tax treatment; the investment is a separate choice. The Roth example assumes qualified tax-free withdrawals. The pre-tax example assumes contributions receive the modeled current tax benefit.

With equal deposits, both start at $1,000 per month, but Roth costs more take-home pay. For equal household cost, the current tax rate matters:

If the current and withdrawal tax rates are the same, those two tax factors cancel in this simplified model. Account limits, eligibility, deductibility, tax-law changes, and taxable-account overflow are not enforced. The app calculates with unrounded values, so displayed arithmetic can differ by a dollar after rounding.

TIPS: the input return is real. The app converts it into a nominal assumption for each year’s inflation path:

These are model inputs before fees, not a guarantee for a specific TIPS bond or fund. Market prices can fluctuate.

Crypto crash stress: the app separately applies an immediate loss to the crypto component at age 62.

This extra stress is not part of the percentile simulation. It assumes no subsequent recovery. The main model does not capture fraud, lost access, or permanent catastrophic failure, and a 0% expected annual crypto return input does not guarantee a stable ending balance.

For expected annual simple return r, annual log-return volatility input σ, annual fee f, and a standard-normal draw z:

The log adjustment connects the selected expected simple return to the lognormal return model. The fee is compounded monthly using its annual factor. For a TIPS allocation, the nominal expected return is recomputed for the inflation assumed in each year.

Mixed-portfolio covariance: equity assets load 0.9 on a shared equity factor; bonds load 0.8 on a shared bond factor; gold has its own independent factor; crypto loads 0.4 on the equity factor, with the rest independent. Residual asset-specific risks are independent. The app squares and sums weighted factor exposures and weighted residual risks, then takes the square root. These are chosen classroom correlations.

Fixed random seeds keep repeats reproducible. Outcomes are distributions for each choice rather than simultaneous realized investment paths. The model excludes changing market regimes, changing correlations, fat tails, employer matching, unplanned withdrawals, and many real-world disruptions.

1. Use one pair of investments and record two different inflation scenarios with the same return/risk inputs and fee.
2. Choose one investment from that pair and select which recorded run the certificate should use.
3. The certificate retrieves that run’s saved outcomes, inflation factor, account comparison, fees, returns, and taxes. It does not substitute later calculator edits.
4. For Roth, the displayed amounts use the simulated ending balances. For pre-tax, they also apply the recorded household-cost scaling and withdrawal tax.
5. Median buying power equals the selected after-tax median divided by the saved inflation factor.
6. The certificate includes your group’s reason, accepted risks, and conditions for reconsidering.

The certificate congratulates the group’s decision-making. Its projected amount is not a guarantee. Smooth U.S. or global economic conditions would not ensure that result, and inflation, recessions, lost income, or other disruptions can affect actual outcomes.

Try this comparison using the fixed baseline: 60/40 has median buying power of $1,471,128, versus $1,635,568 for 80/20. But its lower nominal outcome is $2,475,478, versus $2,387,255 for 80/20. Those are different kinds of evidence; name which column and units you are comparing.

Then test inflation: for the same 60/40 nominal median, buying power falls from $1,272,201 under 4% for ten years then 2.5%, to $822,757 under 4% for all forty years.

Your group’s report: “We choose ___ over ___. Our two numerical comparisons are ___. We accept ___ risk. If ___ changes, we would reconsider.”