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Compound interest formula: A = P(1 + r/n)^(nt), where A = final amount, P = principal, r = annual interest rate (decimal), n = compounding frequency per year, t = years. Example: 10,000 dollars invested at 7 percent compounded monthly for 20 years: A = 10,000 x (1 + 0.07/12)^(12 x 20) = 10,000 x (1.00583)^240 = 40,387 dollars. Common compounding frequencies: annual (n=1), semi-annual (n=2), quarterly (n=4), monthly (n=12), daily (n=365), continuous (A = Pe^rt for maximum). The Rule of 72 approximates doubling time: 72 / interest rate percent. At 7 percent, money doubles every 10.3 years; at 10 percent, every 7.2 years. Long-term historical returns for reference: US stock market (S&P 500) approximately 10 percent nominal (7 percent real after inflation) over 100-plus years; bonds 5 to 6 percent nominal; high-yield savings and CDs 4 to 5 percent (2025 rates post Fed hikes). Albert Einstein allegedly called compound interest the eighth wonder of the world. Starting early matters more than contribution amount: investing 200 dollars per month from age 25 to 65 at 8 percent yields 702,000 dollars; same contributions from 35 to 65 yields 300,000 dollars (less than half, for 75 percent of the contributions).

Retirement savings targets depend on desired lifestyle and retirement age. Fidelity's benchmarks for a comfortable retirement: by age 30 save 1x annual salary, age 40 save 3x, age 50 save 6x, age 60 save 8x, age 67 save 10x annual salary. This assumes 15 percent annual savings rate (including employer match), 1.5 percent wage growth, and withdrawals of 45 percent of pre-retirement income lasting through age 93. Safe withdrawal rate: the classic 4 percent rule (Trinity Study) suggests you can withdraw 4 percent of retirement portfolio annually, adjusted for inflation, with high probability of lasting 30 years. So 1M dollars portfolio supports 40,000 dollars annual withdrawals. Conservative adjustment post 2020: 3.3 to 3.5 percent for longer retirements (35 to 40 years) or early retirement. For FIRE (Financial Independence Retire Early): target 25x annual expenses. 2026 IRS contribution limits: 401(k) 23,500 dollars (plus 7,500 catch-up at 50+), IRA 7,000 dollars (plus 1,000 catch-up at 50+), HSA 4,300 individual or 8,550 family. Social Security provides approximately 40 percent replacement ratio for middle-income earners; plan for the remaining 30 to 50 percent from personal savings. At 62 (earliest claiming age), benefits are reduced 30 percent from full retirement age; waiting until 70 increases benefits by 32 percent above FRA amount — worth it if longevity expectations exceed 78 years.

Fixed-rate mortgage payment formula: M = P[r(1+r)^n] / [(1+r)^n - 1], where M = monthly payment, P = principal, r = monthly interest rate (annual rate / 12), n = number of months. Example: 400,000 dollars loan at 6.5 percent for 30 years: r = 0.065/12 = 0.00542, n = 360. Monthly P+I = 400,000 x (0.00542 x 1.00542^360) / (1.00542^360 - 1) = 2528 dollars per month. Total cost of mortgage: 2528 x 360 = 910,080 dollars, meaning 510,080 dollars in interest over 30 years. Principal-and-interest is only part of PITI (Principal, Interest, Taxes, Insurance). Property taxes typically 1 to 2.5 percent of home value annually (varies by state: NJ 2.49 percent, HI 0.28 percent). Home insurance: 0.35 to 0.75 percent of home value. PMI (private mortgage insurance, required if down payment under 20 percent): 0.3 to 1.5 percent of loan annually. HOA fees if applicable. Total PITI on 400K home with 20 percent down at 6.5 percent mortgage: P+I 2528 + tax 500 + insurance 150 = approximately 3200 dollars per month. Affordability rule: total housing should not exceed 28 percent of gross income (front-end ratio); total debt payments including housing should not exceed 36 percent (back-end ratio). So 3200 per month PITI requires approximately 137K dollars gross annual income (at 28 percent rule). Recast mortgage if you make large lump-sum payments. Refinance if rates drop 0.75 to 1.0 percent or more and you plan to stay 3+ years.

Emergency fund targets range based on income stability and household circumstances. Standard recommendation: 3 to 6 months of essential monthly expenses (not income). For dual-income stable households: 3 months typically sufficient. Single-income or variable income (self-employed, commission-based): 6 to 12 months. Households with children, medical conditions, or in cyclical industries: 6 to 9 months. Calculate essential expenses (not total budget): housing, utilities, food, transportation, insurance, minimum debt payments, childcare, medical. Typical US household essential expenses: 3,500 to 6,500 dollars per month (national median); coastal metros (SF, NYC, Boston) 6,000 to 11,000 dollars per month. For a family with 5,000 per month essentials: 15K (3 months) to 30K (6 months) emergency fund. Where to keep it: high-yield savings account (Marcus, Ally, Wealthfront Cash currently 4.5 to 5 percent APY), money market fund (Vanguard VMFXX 5-plus percent), or CD ladder (1, 3, 6, 12 month CDs rolling). NOT in stocks or volatile investments — you need liquidity and capital preservation. Build up gradually: start with 1,000 dollars starter emergency fund, then tackle high-interest debt (credit cards over 15 percent APR), then build full 3 to 6 month fund. Never use emergency fund for non-emergencies (vacation, down payment) — immediately rebuild if tapped. Keep in separate account from checking to avoid spending temptation.

Net worth = Total Assets - Total Liabilities. Assets include: cash and checking, high-yield savings, emergency fund, investment accounts (401k, IRA, brokerage), real estate at market value, vehicles at current value (depreciating asset), business ownership, HSA, pension present value, collectibles at fair market value. Liabilities: mortgage balance, auto loans, credit card debt, student loans, personal loans, tax debts, HELOC balance. Example: Assets checking 5K + savings 25K + 401(k) 180K + IRA 45K + brokerage 35K + home 475K + car 18K = 783K. Liabilities: mortgage 285K + credit cards 2K + student loans 28K + auto loan 12K = 327K. Net worth = 456K dollars. US median household net worth by age (Federal Reserve 2022 SCF, most recent): under 35: 39K, 35 to 44: 136K, 45 to 54: 247K, 55 to 64: 365K, 65 to 74: 410K. Top quartile at age 45 to 54: approximately 800K; top 10 percent: 2.5M+. Track quarterly using tools like Empower (formerly Personal Capital), Monarch, YNAB, Copilot, or Google Sheets. Focus on trend over time rather than absolute number — increases of 10 to 25 percent annually during wealth-building years are typical for disciplined savers. Key milestones: net worth equal to annual income by age 30, 3x by 40, 6x by 50, 10x by 60 (per Fidelity retirement benchmarks). Exclude primary home from retirement calculations since you need somewhere to live — liquid net worth is a better measure of financial independence readiness.