Nominal and effective rates differ
A nominal annual rate is divided among compounding periods. Effective annual yield includes the within-year interest earned on earlier interest.
Interest equation, rate conversion, and target lab
Connect the quoted rate to growth, taxes, purchasing power, and a target
Compare nominal and effective yield, five compounding frequencies or continuous growth, contribution timing, taxes, inflation, simple-interest and continuous benchmarks, exact doubling time, and the rate or monthly deposit required for a goal.
Plan with context
Interest is a rate, a timing convention, and a changing balance.
A useful interest analysis explains what the quoted rate means, how often it compounds, when cash enters the account, what drag is applied, and whether the resulting balance reaches a real-world goal.
Contribution timing compounds
A beginning-of-period deposit receives one more modeled growth interval than the same deposit made at the end, and this repeats for every contribution.
Simple interest uses a stable base
Simple interest does not add earned interest to the principal used for later calculations. Compound interest does, causing the paths to diverge over time.
Continuous growth is a limit
Continuous compounding uses the exponential function as the mathematical limit of increasingly frequent compounding; ordinary accounts normally use discrete daily or monthly methods.
Tax and inflation answer different questions
Tax drag reduces the amount retained, while inflation converts a future nominal balance into estimated present purchasing power. Both assumptions can change.
Targets can be solved backward
Instead of accepting one projection, solve for the annual rate or starting monthly deposit needed to reach the entered target under the same assumptions.
Included
Starting principal, years and months, monthly and annual contributions, beginning or end timing, five discrete frequencies and continuous compounding, tax on positive interest, inflation, nominal and effective yield, exact doubling time, Rule of 72, target gap, required rate and contribution, four Chart.js paths, and a ledger.
Not included
Variable rates, market losses, fees, withdrawal penalties, contribution limits, tax deferral, capital-gain treatment, institution-specific daily balance and day-count rules, intra-month transactions, or guarantees.
Use it well
Confirm whether the quoted figure is nominal or APY, align deposit timing with actual cash flow, compare after-tax and real results, and stress lower rates before relying on a target date.