Finance formulas

How to use this lab

1. 01Read the expression on the card so you know what the calculator is solving.
2. 02Skim the worked peel for a one-line reality check (fees, compounding, escrow).
3. 03Run a calculator with your numbers. Keep assumptions visible.

Rate labels

How lenders and banks quote yearly cost or yield after fees and compounding.

• APR (Annual Percentage Rate)

  APR explained: what it includes, how it differs from interest rate, and how to compare loan offers correctly.

  EXPRESSION

  APR ≈ (Total Finance Charges / Loan Amount) / (Loan Term in Years) × 100

  WORKED PEELSame 6% note rate: $2k fees ≈ 6.08% APR sketch vs $5k fees ≈ 6.20% APR sketch on a $200k / 30y loan.

  Loan CalculatorGlossary definition

• APY (Annual Percentage Yield)

  APY explained: compounding, how to compare savings products, and why APY is usually higher than APR for the same nominal rate.

  EXPRESSION

  APY = (1 + r/n)^n - 1

  WORKED PEEL12% nominal compounded monthly → APY ≈ (1 + 0.12/12)^12 - 1 ≈ 12.68%.

  Compound Interest CalculatorGlossary definition

• Nominal vs Effective Interest Rate

  Nominal vs effective rate explained with compounding intuition and how to normalize comparisons.

  EXPRESSION

  Effective Rate = (1 + r/n)^n - 1

  WORKED PEEL6% nominal monthly → effective ≈ (1 + 0.06/12)^12 - 1 ≈ 6.17%.

  Interest CalculatorGlossary definition

Housing & loans

Payment math, full housing stack, affordability ratios, insurance add-ons, and refinance timing.

• Amortization

  Amortization explained: how payments split into interest vs principal and why early payments are interest-heavy.

  EXPRESSION

  M = P × [r(1+r)^n] / [(1+r)^n - 1]

  WORKED PEELM = P × [r(1+r)^n] / [(1+r)^n - 1]. Early months are mostly interest; the schedule flips over time.

  Amortization CalculatorGlossary definition

• PITI (Principal, Interest, Taxes, Insurance)

  PITI explained: what's included, what's not (HOA/maintenance), and why PITI matters for true housing cost.

  EXPRESSION

  PITI = Principal + Interest + (Annual Property Taxes / 12) + (Annual Homeowners Insurance / 12)

  WORKED PEELPITI = P&I + taxes/12 + insurance/12. HOA and maintenance usually sit outside the PITI label.

  Mortgage CalculatorGlossary definition

• DTI (Debt-to-Income Ratio)

  DTI explained: housing vs total DTI, why lenders use it, and how to use it safely for affordability planning.

  EXPRESSION

  DTI = (Total Monthly Debt Payments / Gross Monthly Income) × 100

  WORKED PEELDTI = monthly debts ÷ gross monthly income × 100. Lenders often watch housing and total DTI separately.

  House Affordability CalculatorGlossary definition

• PMI (Private Mortgage Insurance)

  PMI explained: when it applies, how it affects monthly cost, and how/when it can drop off.

  EXPRESSION

  PMI Monthly Cost = (Loan Amount × PMI Rate) / 12

  WORKED PEELPMI ≈ (loan × annual PMI rate) / 12 until equity rules let you cancel (often ~20% equity).

  Mortgage CalculatorGlossary definition

• Refinance Break-Even

  Refinance break-even explained: how to compute break-even months and the most common 'term reset' trap.

  EXPRESSION

  Break-Even Months = Total Refinance Costs / Monthly Payment Savings

  WORKED PEELBreak-even months = closing costs ÷ monthly payment savings. Stay shorter than break-even and the refinance loses money.

  Mortgage CalculatorGlossary definition

Investing & tax

Purchasing-power returns and the two tax rates people mix up in planning.

• Inflation and Real Return

  Real return explained: how inflation changes purchasing power and why planning in real terms is more honest.

  EXPRESSION

  Real Return = [(1 + Nominal Return) / (1 + Inflation Rate)] - 1

  WORKED PEEL7% nominal and 3% inflation → real ≈ (1.07 / 1.03) - 1 ≈ 3.88% (not a flat 4% subtract).

  Inflation CalculatorGlossary definition

• Marginal vs Effective Tax Rate

  Tax rates explained: why your marginal rate isn't your average rate and how to interpret bracket breakdowns.

  EXPRESSION

  Effective Tax Rate = (Total Tax Paid / Gross Income) × 100

  WORKED PEELMarginal is the next-dollar bracket. Effective is total tax ÷ taxable income. Effective is almost always lower.

  Income Tax CalculatorGlossary definition