Financial Formulas
All the formulas behind our calculators, explained simply.
Compound Interest
A = P × (1 + r/n)^(n×t)
A = final amount · P = principal · r = annual rate · n = compounding frequency · t = years
With regular contributions: A = P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) - 1) / (r/n)]
Mortgage Payment
M = P × [r(1+r)^n] / [(1+r)^n - 1]
M = monthly payment · P = loan amount · r = monthly rate (annual/12) · n = total payments (years×12)
ROI (Return on Investment)
ROI = ((Final Value - Initial Cost) / Initial Cost) × 100%
Annualized: AROI = ((1 + ROI)^(1/years) - 1) × 100%
Inflation (Purchasing Power)
Future Value = Present Value / (1 + i)^t
i = inflation rate · t = years · Purchasing power decreases exponentially
Passive Income
Annual Income = Investment × Yield Rate
With reinvestment: Portfolio grows at (yield + growth) rate annually. Income = portfolio × yield each year.
₿ Bitcoin DCA
Avg Cost = Total Invested / Total BTC
Each purchase: BTC bought = amount / price at time. Total BTC is sum of all purchases.
Staking Rewards
Rewards = Amount × ((1 + APY/periods)^periods - 1)
periods = compounding periods in duration · Higher frequency = higher effective yield
Mining Profitability
Profit = Revenue - Electricity Cost - Pool Fees
Revenue = coins mined × price · Electricity = power(kW) × hours × $/kWh
Capital Gains Tax
Tax = Capital Gain × Tax Rate
Capital Gain = (Sell Price - Buy Price) × Quantity - Fees
Short-term (<1yr): ordinary income rates · Long-term (>1yr): 0%, 15%, or 20%
Short-term (<1yr): ordinary income rates · Long-term (>1yr): 0%, 15%, or 20%