Investing & Time Value
Explore discounting, compounding and annualized returns.
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Build an intuition for finance with small interactive examples, then try the numbers yourself.
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Follow a suggested order, or explore a concept that interests you.
Bond Basics
Connect coupons and principal to bond prices and yields.
Explore all 12 guidesStart learningCorporate Finance
Connect cash flows, project decisions, valuation and returns.
Explore all 13 guidesStart learningStatistics & Data
Explore averages, volatility, uncertainty and relationships.
Explore all 10 guidesStart learningMacroeconomics
Connect prices and purchasing power with GDP, labor markets, interest and exchange rates.
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70 concepts with interactive examples, linked to calculators or analysis.
Investment
19 guidesCompounding & TimeHow earlier returns earn returnsRecurring InvestmentSeparate initial capital, contributions and growthCompound Annual Growth (CAGR)Annualize beginning-to-ending growthPresent Value & DiscountingWhy future money is discountedFuture Value & GrowthHow today's principal growsNominal & Effective Annual RatesNominal versus effective annual ratesAnnuity Present ValueDiscount a stream of equal paymentsAnnuity Future ValueAccumulate equal paymentsCAPM and market risk premiumsConnect the market premium to required returnPortfolio diversificationCompare how weights change return and volatilitySharpe ratio and risk-adjusted returnsCompare excess return with volatilityBeta and systematic riskUnderstand market sensitivity, the limits of diversification, and beta's role in CAPM.Alpha and active ETFsUse active ETFs to distinguish benchmark excess returns, Jensen alpha, costs, and performance limitations.Dividend discount model DDMEstimate share value from dividend growth and required return.Option payoffs and four basic positionsCompare expiry profit and loss for four option positions.Loan amortization and repayment methodsCompare monthly payments, interest and principal repayment.Maximum drawdown and investment riskExplore peak-to-trough loss, recovery and time underwater.Binomial and Black–Scholes pricingCompare binomial and BSM pricing assumptions.Fama–French three-factor modelExplore market, size and value factor exposures.
Bond
12 guidesYield to Maturity (YTM)Solve YTM from a priceBond Prices & YieldsValue coupons and principal separatelyCurrent YieldCompare annual coupons with priceBond ConvexityWhy duration introduces errorBond DurationDuration versus maturityClean & Dirty Bond PricesQuotes versus settlement amountsYield to Call & Yield to WorstCall timing and redemption change yieldBond Holding-period ReturnCombine coupon income, reinvestment and price changeBond Premium, Discount & ParContractual coupons stay fixed while required returns change. Price brings the two back into balance.Bond Yield ComparisonAre you asking about coupons, maturity, an early call or a sale? Each measure answers a different question.Bond Reinvestment RiskAfter each coupon arrives, what rate can it earn? That can change the final outcome of the same bond.Zero-Coupon BondsWithout interim coupons, return can still come from the difference between purchase price and face value received at maturity.
Corporate finance
13 guidesNet Present Value (NPV)Why future cash flows are discountedInternal Rate of Return (IRR)What a zero crossing of NPV meansPayback PeriodFind the first recovery timeDiscounted PaybackHow discounting changes recovery timeProfitability Index (PI)Present value per dollar investedModified Internal Rate of Return (MIRR)Separate finance and reinvestment ratesBreak-even PointHow each sale covers fixed costsROE & ROAThe questions ROE and ROA answerDuPont AnalysisThe three drivers of ROEDiscounted Cash Flow Valuation (DCF)Forecast PV and terminal PV build valueWACC and financing costsSeparate market-value weights and weighted contributionsEquivalent Annual Annuity (EAA)Convert NPV into EAAXIRR and XNPV: dated cash flowsEvaluate present value and return from dated cash flows.
Statistics & Data Analysis
10 guidesMean & Standard DeviationEqual means can hide different volatilityZ-scoreMeasure signed distance in SD unitsMean Confidence IntervalHow n, spread and confidence change an intervalCorrelation & Co-movementLinear direction and outlier sensitivityLinear Regression & FitHow slope and intercept set the fitted lineStudent’s t-testCompare mean differences with standard errorOne-way ANOVASeparate between and within variationChi-square TestsCompare observed and expected countsDistributions & Critical ValuesRead probability curves and tail areasRegression Inference & ResidualsSeparate fit from coefficient significance
Macroeconomics
16 guidesReal Interest RateSeparate exact real interest from the Fisher approximationInflation & Purchasing PowerSeparate future costs from fixed-money purchasing powerGDP GrowthCalculate two-period real output growthGDP DeflatorDerive the deflator from nominal and real GDPExchange Rates & Currency ChangesIdentify the quote direction and home currencyCPI & the Consumer BasketSeparate index levels, changes and comparison periodsPPI & Price TransmissionDistinguish producer selling prices from consumer pricesUnemployment & the Labor ForceSeparate employment, unemployment, inactivity and excluded peopleGDP & the Expenditure ApproachUnderstand expenditure GDP and inventory accounting across yearsThe Yield CurveRead term spreads in percentage points and basis pointsReal Exchange Rates & PPPDefine quotes, comparable baskets and real exchange ratesPCE Price IndexSeparate MoM from YoYTaiwan Central Bank: Four ObjectivesUnderstand Taiwan's four statutory central-bank objectives through everyday banking, prices and exchange-rate scenarios.The Fed's Dual MandateUnderstand maximum employment, price stability and the policy trade-offs that emerge when inflation and labor-market conditions diverge.Three Monetary Policy ToolsExplore open market operations, discount policy and reserve requirements, while distinguishing textbook mechanisms from current CBC and Fed implementation.FOMC Rate DecisionsRead the FOMC statement, SEP dot plot and Chair's press conference together, distinguishing today's decision from conditional projections and market surprises.
Financial Case Studies
Original finance stories with interactive examples, to connect the numbers with their meaning.
- The Power of Time: What Difference Does Investing 10 Years Earlier Make?Two people invest the same amount for ten years at the same assumed return. Follow their twenty-year story to see what changes when one starts a decade earlier—and keeps holding after contributions stop.
- Higher IRR, Lower NPV? Why Investment Rankings DisagreeWith equal initial outlays, earlier cash recovery gives A a higher IRR while B can create more net present value. Follow the two-year cash flows and see how the cost of capital changes the choice.
- Why Do Longer Bonds Fall More When Yields Rise?Two bonds share a coupon rate but respond differently to rising yields. Follow their cash flows to understand duration, convexity and the limits of a price estimate.
- Same Coupon, Different Return: What Changed?Follow two hypothetical three-year outcomes for the same bond. Separate coupon income, reinvestment and sale gains to see why holding-period return differs from purchase YTM.
- An Active ETF Beats the Market by 3 Points. Is That Skill?Compare two hypothetical ETFs using return, CAPM alpha and Sharpe ratios, then examine official FBCG and IWF annual returns for 2021–2025 without confusing outperformance with manager skill.
- Why Are Prices Still High When Inflation Is Falling?Start with a hypothetical basket priced at 100, then examine official U.S. CPI, PCE and Taiwan CPI history to separate inflation, accumulated price changes and purchasing power.
- Why Can the 10-Year Treasury Yield Rise After a Fed Rate Cut?Examine official data from the September 2024 rate cut through year-end, then distinguish policy rates, Treasury yields, bond prices and holding-period returns.
- Why Does the U.S.–Japan Rate Gap Matter for USD/JPY? Interest Differentials, Exchange Rates and Carry TradesInterest rates determine income in each currency; exchange rates determine what remains when an investment is converted home. Explore capital flows, carry trades and interest parity without treating a rate gap as a forecast.
- Does a Higher PPI Necessarily Raise CPI? From Production Costs to Consumer PricesPrice signals pass through trading stages and business decisions before they may affect consumer spending. A hypothetical food supply chain illustrates absorption, pass-through and timing.
- Same average returns, different retirement outcomes?Two retirees share the same starting wealth and returns. Their withdrawal paths tell different stories.
- Lower mortgage rates: should you prepay or refinance?A 5,000,000 mortgage and 500,000 cash: compare keeping, prepaying and refinancing fairly.