nestegg.money

Monthly loan amortization schedule and summary.

Time and interest saved by paying a fixed extra amount every month on a loan, versus the baseline schedule.

Future value of a single lump sum compounded annually.

Future value of a fixed monthly contribution, optionally stepping up each year.

Compound annual growth rate between two values over a number of years.

Fraction of income saved (savings divided by income).

Convert an amount using a rate supplied by the caller (units of target currency per unit of source).

Value after compounding down (or up) at a yearly percentage rate over a number of years.

Straight-line depreciation: value falling evenly to a salvage value over a useful life.

FIRE target nest egg from annual spend and a safe withdrawal rate (default 4%), plus the gap from today and the years to reach it given optional savings and growth.

Inverse of contributions: the fixed monthly amount needed to reach a target future value over a number of months, given an optional starting balance.

Convert a nominal amount to today's purchasing power (real), or with toNominal inflate a real amount forward, at a given annual inflation rate.

Convert a nominal annual rate to the effective annual rate (APY) for a compounding frequency, or with toNominal recover the nominal rate from an APY.

Net present value of a cashflow series (index 0 is today; outflows negative) discounted at a per-period rate.

Internal rate of return: the per-period rate that zeroes the NPV of a cashflow series.

Refinance break-even: monthly saving, whole months to recoup closing costs, and (if remainingMonths given) the net saving over the remaining term.

Months of runway: liquid savings divided by monthly expenses.

Maximum loan and home price the income supports: the DTI cap on gross monthly income (less existing debts) sets the payment, whose present value at the rate and term is the loan.

Multi-debt payoff plan under a fixed monthly budget.

How many years a balance lasts while withdrawing from it: the balance grows each year, then the withdrawal (optionally stepping up) is taken.

Present value of a single future amount discounted annually.

Annual return needed to grow a starting value to a target over a number of years, optionally with a fixed annual contribution.

Bond yield to maturity: the nominal annual yield that prices a bond at the given price, with periodic coupons and face returned at maturity.

Progressive tax from caller-supplied brackets.

Convert between margin and markup.

Compound growth at any frequency, with an optional contribution each period (paid at period end).

German net (Netto) salary from gross (Brutto).

Exact German net (Netto) salary from annual gross (Brutto) for tax years 2023-2026.

German flat tax on capital income (Abgeltungsteuer, §32d EStG) for tax years 2023-2026 with the year's Sparerpauschbetrag built in.

German child benefit (Kindergeld) for 2023-2026: the year's flat monthly amount per child (uniform since 2023), as monthly and annual totals.

German Midijob / Uebergangsbereich (paragraph 20 Abs.

German pension points (Entgeltpunkte, paragraph 63 SGB VI) for 2023-2026: points earned from an annual gross via the year's Durchschnittsentgelt (capped at the contribution ceiling), the aktueller Rentenwert for both halves of the year, and optionally the gross monthly state pension for a total point count.

Value-added tax (MwSt/USt, sales tax) on a price.

Return on investment: total percent gain, plus the annualized rate when a holding period in years is given.

Real (inflation-adjusted) return from a nominal rate via the Fisher relation: (1+nominal)/(1+inflation) - 1.

Mean, sample variance, and sample standard deviation (n-1) of a series of returns.

Sharpe ratio: excess mean return per unit of volatility, (mean - riskFree) / stdev.

Maximum drawdown of a value series: the largest peak-to-trough decline, as a positive percent.

Holding-period return: (income + capital gain) / starting value, in percent.

Effect of an annual fee: the compounded balance at the gross rate vs net of the fee, and the amount lost to fees.

Dollar-cost averaging: buying a fixed amount each period at the given prices.

Price of a coupon bond given a yield: present value of the coupons plus the face at maturity.

Current yield: the annual coupon as a percent of the bond's current price.

Macaulay duration (PV-weighted average time of cashflows, in years) and modified duration (price sensitivity to yield).

Bond convexity (years^2): the curvature of price with respect to yield, used alongside duration.

Price of a zero-coupon bond: face value discounted to today at the yield.

Accrued interest since the last coupon: the annual coupon pro-rated by days elapsed over the day-count basis.

Black-Scholes price of a European call or put option, plus d1/d2.

Black-Scholes greeks for a European option: delta, gamma, vega (per 1% vol), theta (per day), rho (per 1% rate).

Put-call parity: given one option price, returns both.

Break-even underlying price at expiry: strike + premium for a call, strike - premium for a put.

Split an option premium into intrinsic value (in-the-money amount) and time value.

Present value of an ordinary annuity (level payment at each period end).

Future value of an ordinary annuity.

The level payment that amortizes a present value over n periods (the loan-payment formula).

Present value of a level or growing perpetuity: payment / (rate - growth).

Years to double: the rule-of-72 estimate (72/rate) and the exact figure (ln2 / ln(1+rate)).

Simple payback period: periods until cumulative cashflows recover the initial cost, interpolated within the crossing period.

Discounted payback period: like payback-period but each cashflow is discounted at the per-period rate.

Modified internal rate of return: negatives financed at financeRate, positives reinvested at reinvestRate.

Date-aware net present value: each amount discounted by its fractional years (act/365) from the first cashflow's date.

Date-aware internal rate of return: the annual rate that zeroes the XNPV of irregular dated cashflows.

Effective APR including upfront fees: the note-rate payment priced against the net proceeds (amount - fees).

Interest-only monthly payment on a balance.

Balloon loan: payment based on a long amortization, with the balloon being the balance still due after the shorter balloon term.

Loan-to-value ratio, percent (loan / property value).

Debt-to-income ratio, percent (monthly debt / gross monthly income).

Months to clear a credit-card balance at a fixed monthly payment, plus interest paid.

Mortgage points break-even: the upfront cost to buy down the rate, the monthly payment saving, and the whole months to recoup it.

Biweekly mortgage acceleration: paying half the monthly payment every two weeks.

Capitalization rate: net operating income as a percent of property value.

Cash-on-cash return: annual pre-tax cash flow as a percent of the cash invested.

Net operating income: gross rental income less vacancy and operating expenses.

Gross rent multiplier: price divided by gross annual rent.

Debt service coverage ratio: net operating income divided by annual debt service.

Weighted average cost of capital: equity and after-tax debt weighted by the capital structure.

Break-even volume: fixed costs divided by the per-unit contribution (price - variable cost), plus the revenue at that volume.

Contribution margin per unit and as a percent of price.

Current ratio: current assets over current liabilities.

Quick (acid-test) ratio: (current assets - inventory) over current liabilities.

Return on equity, percent: net income over shareholders' equity.

Return on assets, percent: net income over total assets.

Declining-balance depreciation: a fixed percent of the reducing book value, for a given year.

Double-declining-balance depreciation: 2/usefulYears of the book value each year, not falling below salvage.

Sum-of-the-years'-digits depreciation: the depreciable base weighted toward the early years.

Units-of-production depreciation: the depreciable base spread over total expected units, charged by the units used this period.

Net worth: assets minus liabilities.

The 50/30/20 budget split of monthly income into needs, wants, and savings.

Tip and split: the tip amount, the total, and the per-person share.

A single percentage discount: the amount off and the final price.

Stacked discounts applied in order: the final price and the effective single discount rate.

Percentage change from one value to another.

Unit price: price divided by quantity (for comparing pack sizes).

Annualize an hourly rate (and the monthly equivalent).

Hourly rate implied by an annual salary.

After-tax yield: a yield reduced by the tax rate.

Tax-equivalent yield: the taxable yield that matches a tax-free (e.g.

Coast FIRE: whether the current nest egg, left to grow untouched to retirement, already reaches the FIRE target.

Barista FIRE: the nest egg needed when part-time income covers part of the spending, so the portfolio only funds the remainder at the safe withdrawal rate.