Interest Calculator

In-Depth Guide

Interest is the price of money, and whether you are earning it in a savings account or paying it on a student loan, the mathematics is the same small family of formulas taught in every time-value-of-money chapter. Simple interest, governed by I = P · r · t, still applies to most short-term auto loans, certain bonds, and many private loans originated in the United States. Compound interest, A = P · (1 + r/n)^(n·t), governs virtually every savings account, certificate of deposit, credit card, and index fund return. The choice of compounding frequency n — daily, monthly, quarterly, annually — is not cosmetic: a 5% APR compounded daily on a $10,000 balance finishes a year at $10,512.67 versus $10,500.00 compounded annually, a spread that widens to thousands of dollars over decades. FastTool's interest calculator handles both models, converts between APR and APY per Federal Reserve Regulation Z, and shows a full amortisation-style breakdown.

Why This Matters

Consumer finance disclosures mandate APR on credit cards and loans under Regulation Z of the Truth in Lending Act, while savings accounts disclose APY under Regulation DD of the Truth in Savings Act. The two numbers describe the same dollar flow only when compounding is annual — in practice they differ, sometimes by 20 basis points on a daily-compounded high-yield savings account. Understanding which formula applies to which product prevents the two classic retail mistakes: over-estimating savings growth by confusing APR with APY, and under-estimating debt cost by treating a daily-periodic-rate credit card as if it compounded monthly.

Real-World Case Studies

• Emergency fund growth. A small restaurant owner in London parks £18,000 in a fixed-term account paying 4.6% AER for two years. The calculator under AER (annual compounding by UK definition) returns £19,712.28 at maturity — an £848 premium over an equivalent simple-interest product. The exact figure lets her model how much of that matures in time to fund a planned kitchen refit without dipping into working capital.
• Student loan payoff. A graduate with a $28,000 federal Direct Unsubsidised loan at 6.54% daily compounding estimates three years of accrued interest during a deferment at roughly $5,900, pushing the balance past $33,900 before repayment starts. Seeing the number in advance motivates her to make interest-only payments during deferment, saving roughly $400 in future capitalisation effects once repayment begins under the standard 10-year repayment plan.
• Teaching compound interest. A high-school economics teacher demonstrates the rule of 72 against the exact compound formula. At 8% annual growth the rule predicts doubling in 9 years; the exact calculator returns 9.006 years. At 18% credit card debt the rule predicts 4 years; the exact formula returns 4.19 years. The worked difference shows students why rules of thumb break down at higher rates.

Technical Deep Dive

Simple interest is straightforward: I = P·r·t where r is a decimal rate per period and t is the number of periods. Compound interest uses A = P·(1 + r/n)^(n·t); the interest earned is A - P. Converting APR to APY follows APY = (1 + APR/n)^n - 1, which for 12.99% APR compounded daily (n=365) returns roughly 13.87% APY. For continuous compounding the limiting formula is A = P·e^(r·t), used in option pricing under Black-Scholes and some bond valuations per CFA curriculum. Edge cases: US credit cards typically quote a nominal APR but compound daily using a daily periodic rate APR/365, producing a slightly higher effective rate; UK savings quote AER which is annualised compounding; leap years can shift daily compounding by one day of interest accrual; and some old-style loans use actual/360 day-count conventions per ISDA definitions, making a nominal 6% APR behave like 6.083% over a 365-day year. Always match the calculator's compounding frequency to the product's disclosure to avoid a meaningful error on long horizons.