Interest Rate Calculators for Borrowers, Savers and Investors

APR (Annual Percentage Rate) is the simple annualized rate without compounding. APY (Annual Percentage Yield) is the effective rate including compounding — used in US savings disclosure. EAR (Effective Annual Rate) is the academic term for the same concept as APY. The formulas: APR = nominal annual rate; APY/EAR = (1 + APR/n)^n − 1, where n is the compounding frequency. A 6% APR compounded daily produces a 6.18% APY. The gap between APR and APY widens as compounding frequency increases, but plateaus quickly — daily vs continuous compounding differs by less than 0.001 percentage points at typical consumer rates. Critical comparison rule: never compare APR of one product to APY of another — the comparison is meaningless. Loans are quoted in APR, savings in APY, and you must convert one to match the other before fair comparison.

Nominal rates ignore inflation; real rates account for it. The Fisher equation: (1 + Nominal) = (1 + Real) × (1 + Inflation), solved for Real = (1 + Nominal)/(1 + Inflation) − 1. A 5% nominal savings rate in a 3% inflation environment is only 1.94% real. The simpler approximation Real ≈ Nominal − Inflation works fine for low rates and short horizons but breaks down at high rates and long horizons — at 12% nominal and 8% inflation, the approximation gives 4% real but the correct Fisher equation gives 3.70% real. Real rates can be negative — a 3% savings account in a 6% inflation environment loses 2.83% of purchasing power per year. Inflation-protected securities (TIPS in US, Index-Linked Gilts in UK, Real Return Bonds in Canada) target a real return directly, removing inflation risk from the equation.

On a 30-year mortgage, each 100 basis points (1%) of rate change costs roughly $60/month per $100K of loan in payment, and ~$24K/$100K in lifetime interest. A $400K mortgage moving from 6% to 7% adds $263/month and $95K lifetime cost. On a 5-year auto loan, each 100bps adds ~$2.50/month per $10K — much smaller absolute impact but a meaningful percentage on payment-strained budgets. On credit cards (typically 18-28% APR), the rate level dominates payoff math more than 100bps changes — a 24% to 22% drop saves only 8% on interest paid over a 5-year payoff, while moving from minimum payments to fixed payments saves 80%+. Rate sensitivity is highest at the start of any amortizing loan and decreases as principal pays down. For variable-rate products (HELOC, ARM, variable savings), always run a stress test at +200-300 basis points above current.

Compounding frequency affects effective rate (APY) but the impact is small and rapidly diminishing. On 5% nominal: annual compounding = 5.000% APY, quarterly = 5.094%, monthly = 5.116%, daily = 5.127%, continuous = 5.127%. The leap from annual to monthly captures most of the benefit; monthly to continuous adds less than 0.012 percentage points. Banks marketing 'daily compounding' as a major selling point are exploiting consumer confusion — the actual benefit over monthly is negligible. What does matter: nominal rate level (5% vs 5.5% is a real 50bps difference), fee structure (account fees that exceed interest earned), and time horizon (compounding effects accumulate over years, not months). When comparing savings products, focus on APY disclosed under Reg DD (US) or equivalent disclosure rules elsewhere — that figure already includes whatever compounding the bank uses.