Methodology

We believe in transparency. Here's exactly how our calculators work, what assumptions we make, and why.

Compound Interest Calculator

Formula

A = P(1 + r/n)^(nt) + PMT × ((1 + r/n)^(nt) - 1) / (r/n)

Where A is the final amount, P is the principal, r is the annual rate, n is compounding frequency, t is time in years, and PMT is the periodic payment.

Assumptions

  • Contributions are made at the end of each period
  • Interest rate remains constant
  • No taxes or fees are deducted

Retirement Calculator

Approach

We project future savings using compound growth with regular contributions, then compare to the amount needed to generate your desired income at your chosen withdrawal rate.

Key Formulas

Amount Needed = Desired Annual Income / Withdrawal Rate
Future Value = Current Savings × (1 + r)^n + Monthly × ((1 + r)^n - 1) / r

Assumptions

  • Default 4% withdrawal rate (based on Trinity Study)
  • Returns are nominal (not inflation-adjusted by default)
  • No Social Security or pension income included
  • Taxes not accounted for in projections

Buy vs Rent Calculator

Approach

We compare total wealth after the holding period under both scenarios. For buying, this includes home equity minus costs. For renting, this includes invested savings.

Buying Scenario Includes

  • Mortgage payments (principal + interest)
  • Property taxes (% of home value)
  • Homeowners insurance
  • Maintenance (% of home value)
  • Home appreciation
  • Closing costs (buying and selling)

Renting Scenario Includes

  • Monthly rent with annual increases
  • Renters insurance
  • Investment of down payment and monthly savings

Rental Property ROI Calculator

Key Metrics

Cash-on-Cash Return = Annual Cash Flow / Total Cash Invested
Cap Rate = Net Operating Income / Property Price
Total ROI = (Cash Flow + Principal Paydown + Appreciation) / Investment

Notes

  • Vacancy is expressed as a percentage of gross rent
  • Tax benefits (depreciation, deductions) not included
  • Appreciation is speculative and not guaranteed

Coast FIRE Calculator

Formula

Coast FI Number = Target / (1 + real_return)^years_to_retirement

Assumptions

  • Uses real (inflation-adjusted) returns
  • Default real return assumption: 5-7%
  • Assumes you'll work until traditional retirement age
  • Does not account for sequence of returns risk

Dividend Growth Calculator

Key Formulas

Annual Dividend = Portfolio Value × Dividend Yield
Yield on Cost = Current Dividend / Original Investment
Future Dividend = Current Dividend × (1 + Growth Rate)^Years

Assumptions

  • Dividend growth rate remains constant
  • No dividend cuts or suspensions occur
  • Stock price grows at the specified rate
  • Taxes on dividends not included

DRIP Forecast Calculator

Approach

Simulates automatic dividend reinvestment by calculating dividends each period, converting them to fractional shares at the current price, and compounding forward.

Key Formulas

New Shares = Dividend Received / Share Price
Total Shares(n) = Total Shares(n-1) + DRIP Shares + Purchased Shares

Assumptions

  • Fractional shares are available (most modern brokers support this)
  • Dividends are reinvested immediately at current price
  • No transaction fees on DRIP purchases
  • Dividend and price growth rates remain constant

Emergency Fund Calculator

Approach

Calculates a personalized emergency fund target based on monthly expenses and individual risk factors, then projects time to reach the goal.

Key Formula

Target = Monthly Expenses × Recommended Months

Risk Factors Considered

  • Job stability (stable, moderate, variable income)
  • Number of income sources (single vs dual income)
  • Dependents and financial obligations
  • Industry volatility and employment market

Vegetable Yield Savings Calculator

Key Formulas

Harvest Value = Sum(Plants × Yield per Plant × Store Price)
Net Savings = Harvest Value - (Startup Costs / Years) - Annual Costs
Effective Hourly Rate = Net Savings / (Hours per Week × Season Weeks)

Assumptions

  • Yields are estimates and vary by climate, soil, and skill
  • Store prices reflect typical grocery costs (may be lower than organic)
  • Startup costs amortized over 5 years by default
  • Does not account for crop failures, pests, or weather events
  • Water costs vary by region and are not included

Savings Goal Calculator

Key Formulas

Monthly Needed = (Goal - Current) / ((((1 + r)^n) - 1) / r)
Final Balance = Current × (1 + r)^n + Monthly × (((1 + r)^n - 1) / r)

Where r is the monthly interest rate and n is the number of months.

Assumptions

  • Contributions made at end of each month
  • Interest rate remains constant
  • Does not account for inflation
  • Taxes on interest not included

Dollar Cost Averaging Calculator

Approach

Simulates periodic investments at fluctuating prices. Prices are generated using a random walk with user-specified volatility, trending from start to end price.

Key Formulas

Shares Purchased = Investment Amount / Price at Purchase
Average Cost = Total Invested / Total Shares
Final Value = Total Shares × Final Price

Assumptions

  • Price movements are simulated (not historical data)
  • Dividends not included in returns
  • No transaction fees
  • Fractional shares available

401(k) Optimizer Calculator

Key Formulas

Employee Contribution = Salary × Contribution %
Employer Match = min(Contribution %, Match Limit) × Match Rate × Salary
Tax Savings (Traditional) = Contribution × Marginal Tax Rate

Assumptions

  • 2024 IRS contribution limits ($23,000 employee, $69,000 total)
  • Employer match vests immediately (no vesting schedule)
  • Uses simplified tax brackets
  • State taxes not included

Expense Ratio Impact Calculator

Key Formulas

Net Return = Gross Return - Expense Ratio
Future Value = P(1 + net_r)^n + PMT × (((1 + net_r)^n - 1) / net_r)
Lifetime Cost = High-Fee FV - Low-Fee FV

Assumptions

  • Both funds have identical gross returns
  • Expense ratios remain constant
  • No load fees or transaction costs
  • Taxes not included

Capital Gains Tax Calculator

Key Formulas

Capital Gain = Sale Price - Cost Basis
Tax (Short-term) = Gain × Ordinary Income Rate
Tax (Long-term) = Gain × LTCG Rate (0%, 15%, or 20%)

2024 Long-term Capital Gains Brackets

  • 0% rate: Single up to $47,025 / Married up to $94,050
  • 15% rate: Single $47,026-$518,900 / Married $94,051-$583,750
  • 20% rate: Above those thresholds

Assumptions

  • Federal taxes only (state taxes vary)
  • 3.8% Net Investment Income Tax not included
  • Does not account for capital loss offsets

Social Security Timing Calculator

Key Formulas

Early Reduction = 6.67%/year (first 3 years) + 5%/year (additional years)
Delayed Credit = 8% per year (up to age 70)
Lifetime Benefits = Monthly Benefit × 12 × (Life Expectancy - Claiming Age)

Break-Even Analysis

Compares cumulative benefits at different claiming ages to find when waiting becomes advantageous.

Assumptions

  • Full Retirement Age assumed at 67
  • Does not include COLA adjustments
  • Spousal and survivor benefits not modeled
  • Taxes on benefits not included

Roth Conversion Calculator

Key Formulas

Conversion Tax = Amount × Current Marginal Tax Rate
Roth Future Value = (Amount - Tax if paid from IRA) × (1 + r)^n
Traditional After-Tax = Amount × (1 + r)^n × (1 - Retirement Tax Rate)

Assumptions

  • Tax rates remain as specified (current and retirement)
  • Roth 5-year rule is satisfied before withdrawal
  • State taxes not included
  • RMD impacts not modeled
  • Medicare IRMAA surcharges not considered

Retirement Withdrawal Calculator

Key Formulas

Withdrawal Rate = Annual Withdrawal / Portfolio Value
Portfolio(n+1) = Portfolio(n) × (1 + return) - Withdrawal × (1 + inflation)^n
Years Until Depletion = Solve for n where Portfolio = 0

Assumptions

  • Uses constant average returns (no sequence risk modeling)
  • Withdrawals adjusted for inflation annually
  • No Social Security or pension income included
  • Taxes on withdrawals not accounted for

Subscription Audit Calculator

Key Formulas

Monthly Cost = Sum(All Subscriptions normalized to monthly)
Annual Cost = Monthly Cost × 12
Potential Savings = Sum(Non-essential Subscriptions)

Approach

Users enter subscriptions with cost, frequency, category, and essential/non-essential status. The calculator normalizes all costs to monthly and annual views, with category breakdowns.

Latte Factor Calculator

Key Formulas

Daily Cost = Sum(Each expense cost × frequency / 365)
Future Value = Monthly Savings × (((1 + r)^n - 1) / r)

Concept

Based on David Bach's "Latte Factor" concept: small daily expenses, when invested instead, can grow to substantial amounts over time due to compound growth.

Assumptions

  • Default 7% annual return (historical stock market average)
  • Expenses continue at constant rate
  • Investment returns are constant (no volatility)
  • Taxes on investment gains not included

Side Hustle ROI Calculator

Key Formulas

Monthly Profit = Revenue - Monthly Expenses
Effective Hourly Rate = Monthly Profit / (Hours/Week × 4.33)
Opportunity Cost = Hours × Alternative Wage
Break-Even Months = Startup Costs / Monthly Profit
ROI = (Annual Profit / Total First Year Investment) × 100

Assumptions

  • Revenue and expenses remain constant
  • Hours worked are tracked accurately
  • Alternative wage represents realistic opportunity cost
  • Self-employment taxes not included in calculations
  • Non-financial benefits (flexibility, passion) not quantified

Important Disclaimer

All calculators on PennyMath are for educational and informational purposes only. They are not financial advice.

  • Past performance does not guarantee future results
  • Actual returns will vary based on market conditions
  • Tax implications vary by situation and location
  • Always consult a qualified financial advisor for personalized advice