Finance formulas & glossary

These are the terms and formulas that show up across finance calculators. Use this as a reference when a calculator asks for a rate, a time horizon, or “what counts” as monthly housing cost.

Finance calculatorsAPR vs APY guide

Glossary (quick links)

APR (Annual Percentage Rate)
APR explained: what it includes, how it differs from interest rate, and how to compare loan offers correctly.
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.
Nominal vs Effective Interest Rate
Nominal vs effective rate explained with compounding intuition and how to normalize comparisons.
Amortization
Amortization explained: how payments split into interest vs principal and why early payments are interest-heavy.
DTI (Debt-to-Income Ratio)
DTI explained: housing vs total DTI, why lenders use it, and how to use it safely for affordability planning.
PITI (Principal, Interest, Taxes, Insurance)
PITI explained: what's included, what's not (HOA/maintenance), and why PITI matters for true housing cost.
PMI (Private Mortgage Insurance)
PMI explained: when it applies, how it affects monthly cost, and how/when it can drop off.
Refinance Break-Even
Refinance break-even explained: how to compute break-even months and the most common 'term reset' trap.
Inflation and Real Return
Real return explained: how inflation changes purchasing power and why planning in real terms is more honest.
Marginal vs Effective Tax Rate
Tax rates explained: why your marginal rate isn't your average rate and how to interpret bracket breakdowns.

APR vs APY

APR is typically a nominal annual rate used for borrowing comparisons (often including fees). APY includes compounding and is commonly used for savings/investments.

Effective/APY relationship (conceptual): \( (1 + r/m)^m - 1 \)

Nominal vs effective rate

Nominal is the stated rate. Effective is what you actually pay/earn after compounding frequency is applied.

Effective rate: \( (1 + r/m)^m - 1 \)

PITI

PITI = Principal + Interest + Taxes + Insurance. It’s the foundation of monthly housing cost. HOA and maintenance reserve are usually separate.

Use: Mortgage Calculator

DTI (Debt-to-income)

DTI measures monthly debt obligations relative to income. For affordability, consider both housing-only and total DTI.

Use: House Affordability Calculator

Amortization (loan payment formula)

Standard fixed-payment loan formula (monthly payment):

\( M = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1} \)
Where \(P\) = principal, \(r\) = periodic rate, \(n\) = number of payments.
Use: Amortization Calculator