// METHODOLOGY

How our finance calculators work.

We use the same financial formulas taught in CFA and CFP certification programs — with full floating-point precision, 2024 IRS brackets, and zero intermediate rounding. Here's exactly how every calculation works.

// MATH STANDARDS

Precision standards.

Most web calculators use simplified formulas or round intermediate numbers to two decimal places at every step. Over long time horizons, this creates significant drift. WealthifyX carries full precision through every calculation and only rounds at the final display step.

Zero Rounding Drift

Calculations run at 16-decimal precision. Display rounding happens once — at the output.

2024 IRS Limits Applied

Retirement calculators enforce the current contribution limits and tax brackets automatically.

Standard TVM Equations

Institutional Time Value of Money formulas for all growth projections — not simplified shortcuts.

What
Typical
WealthifyX
Intermediate rounding
Yes — 2 decimal places
Never
Compounding frequency
Monthly only
Daily / Monthly / Quarterly / Annual
IRS limit enforcement
Not applied
2024 limits on every retirement tool
Formula standard
Simplified approximation
IEEE 754 full precision
Tax bracket stacking
Flat rate on full gain
Gains stacked on ordinary income
30-year drift
Up to 3–8% error
None
// FORMULARY

Formula transparency.

The exact mathematical logic powering all 8 calculators.

// FORMULA — COMPOUND INTEREST
A = P(1 + r/n)^(nt)
With contributions: A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]
AFinal balance (future value)
PPrincipal — initial investment
rAnnual interest rate as a decimal
nCompounding periods per year (12 = monthly, 365 = daily)
tTime in years
PMTMonthly contribution amount
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// FORMULA — INVESTMENT
FV = PV(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]
FVFuture value — final portfolio worth
PVPresent value — initial investment
rAnnual return rate as a decimal
nCompounding periods per year
tTime in years
PMTPeriodic contribution amount
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// FORMULA — ROTH IRA
FV = B₀(1 + r)^t + C × [((1 + r)^t − 1) / r]
FVTax-free balance at retirement
B₀Existing Roth IRA balance today
rAnnual return rate (7% default — S&P inflation-adjusted)
tYears from current age to retirement age
CAnnual contribution — capped at 2024 IRS limit ($7,000 / $8,000 age 50+)
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// FORMULA — 401K
FV = B₀(1 + r)^t + C_total × [((1 + r)^t − 1) / r]
C_total = min(salary × emp%, IRS_limit) + salary × min(emp%, match_ceiling%) × match_rate%
FVPre-tax 401k balance at retirement
B₀Existing 401k balance
rAnnual return rate
tYears to retirement
C_totalTotal annual contribution — employee + employer match
IRS_limit$23,000 (2024) · $30,500 age 50+ with catch-up
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// FORMULA — SAVINGS GOAL
C = (Goal − B₀(1+r)^n) ÷ [((1+r)^n − 1) ÷ r]
Time mode: balance iterated month-by-month until balance ≥ Goal
CRequired monthly contribution to reach Goal in n months
B₀Current savings — starting balance
rMonthly return rate (annual ÷ 12)
nNumber of months to target date
GoalTarget savings amount
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// FORMULA — OPTIONS P&L AT EXPIRY
Long Call: P&L = (max(0, S − K) − P) × 100 × N
Long Put: P&L = (max(0, K − S) − P) × 100 × N · Short: flip sign
SStock price at expiry
KStrike price of the option
PPremium per share (paid for long, received for short)
NNumber of contracts (1 contract = 100 shares)
BEBreakeven — Long Call: K + P · Long Put: K − P
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// FORMULA — CAPITAL GAINS TAX
Federal Tax = calcLTCG(gain, ordinaryIncome, filingStatus)
NIIT = min(gain, max(0, MAGI − threshold)) × 3.8% · Total = Federal + NIIT + State
LTCG0% / 15% / 20% — gains stacked on top of ordinary income (2024 brackets)
STCGOrdinary income rate 10%–37% — applied as marginal tax on gain
NIIT+3.8% on gains where MAGI > $200k single / $250k married joint
StateFlat rate applied to total gain (optional, user-entered)
Net ProfitGain − Federal Tax − NIIT − State Tax
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// FORMULA — DIVIDEND & DRIP
DRIP: new shares = (S × DPS/4) ÷ P (quarterly)
Yield on Cost = (Final Annual Income ÷ Original Cost Basis) × 100
SCurrent shares owned — grows with each DRIP reinvestment
DPSAnnual dividend per share — grows at dividend growth rate each year
PCurrent share price — grows at stock growth rate each year
YOCYield on Cost — annual income return on original purchase price
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// PRECISION DETAILS

Edge cases we handle correctly.

Zero contribution amounts

If monthly contribution is left blank or set to 0, every formula reduces to pure compound growth with no PMT term. No divide-by-zero errors, no NaN outputs — validated before any calculation runs.

Very long time horizons

JavaScript's IEEE 754 double-precision handles values up to 10^308. Even at 50 years with a 12% annual rate, calculation precision is completely unaffected.

High compounding frequencies

Daily compounding (n=365) uses the exact daily rate — not approximated using continuous compounding shortcuts. This matters most at high rates over long periods.

Tax bracket stacking

Capital gains are stacked on top of ordinary income — not taxed from $0. The LTCG engine identifies how much of the gain falls in each bracket and applies the correct rate to each portion.

// DISCLOSURES

Important caveats.

Inflation

Unless explicitly stated, results are shown in nominal terms — not adjusted for inflation. A $1M balance in 30 years will have significantly less purchasing power than $1M today. Subtract your expected inflation rate (~3%) from the return rate to approximate real returns.

Taxation

Growth calculators show pre-tax returns unless they are explicitly a tax calculator. Actual take-home amounts will vary based on your account type (taxable, Roth, traditional) and applicable tax law.

Past Performance

Historical rates — like the S&P 500's ~10.7% average — are reference points, not guarantees. Actual future returns will vary based on market conditions, fees, and your specific holdings.

Not Financial Advice

WealthifyX calculators are educational tools. They do not constitute financial, tax, or investment advice. Consult a qualified advisor before making investment decisions.

// FAQ

Common questions.

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