{ "schemaVersion": 1, "slug": "compound-interest-calculator", "category": "finance", "kind": "implementation", "independentValidation": false, "implementationHash": "a7e6028e2917f53136967559a69f772013e2624e676694b413b57e969c10d05e", "provenance": "Generated from the calculation contract used by the published page. Publication is not external validation.", "sourceFiles": [ "data/calculators/compound-interest-calculator.json", "src/engine.js" ], "runtimeSource": "/sources/engine.txt", "runtimeHash": "5c888d8898afbdee36267bb9977829e1e2ac568f6677c8ee87469c139864645c", "scope": "The compute function records implemented equations, constants, lookup tables and custom rules. Inputs record defaults and allowed values; outputs record precision and units. Defaults are examples, not recommendations. General background references are not evidence for this specific algorithm.", "publishedFormula": { "formula": "A = P·b^(n·t) + Σⱼ₌₁ᴺ C·b^(n·(t−(j−δ)/f)); b = 1+r/n; N = ⌊f·t⌋; I = A−(P+C·N)", "vars": [ [ "A", "Final balance" ], [ "P", "Initial amount" ], [ "r", "Annual interest rate / 100" ], [ "n", "Compounding frequency" ], [ "t", "Years" ], [ "C", "Recurring deposit" ], [ "f", "Deposit frequency" ], [ "N", "⌊f·t⌋" ], [ "δ", "0: Period end; 1: Period beginning" ], [ "I", "Interest earned" ] ], "note": "Growth uses a constant nominal annual rate and fractional compounding periods between deposit dates. Monthly or annual deposits use the selected start/end timing; only complete deposit periods count. Taxes, fees and inflation are excluded; returns are not guaranteed. B−A compares the selected final balances, which may have different time horizons. The annual table and growth chart show A." }, "externalEvidence": { "reviewedAt": "2026-10-22", "sources": [ { "name": "OpenStax — Compound interest equation", "url": "https://openstax.org/books/college-algebra-2e/pages/6-key-equations" }, { "name": "SEC Investor.gov — Compound interest inputs", "url": "https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator" } ], "implementationHash": "a7e6028e2917f53136967559a69f772013e2624e676694b413b57e969c10d05e", "basis": "Apply the nominal annual rate divided by the compounding frequency to the initial balance. Each recurring deposit grows from its scheduled beginning or end of a complete month or year; a partial final deposit period adds growth but no new deposit. At 0% interest, an initial 1000 plus twelve monthly deposits of 100 ends at 2200 after one year. Total deposited includes the initial amount; interest is final balance minus that total. Scenario B uses its own rate, deposit and duration, while the annual table and chart show A. A B − A difference with different durations is a balance comparison, not an equal-time return comparison. Supported limits are 1 billion initially, 10 million per deposit, 0–100 years and −100% to 100% nominal annual interest. Taxes, fees and inflation are excluded; returns are not guaranteed.", "limitations": "Growth uses a constant nominal annual rate and fractional compounding periods between deposit dates. Monthly or annual deposits use the selected start/end timing; only complete deposit periods count. Taxes, fees and inflation are excluded; returns are not guaranteed. B−A compares the selected final balances, which may have different time horizons. The annual table and growth chart show A." }, "contract": { "compute": "const project=(P,rate,t,C,f,timing)=>{\n const b=1+rate/100/compounds, count=Math.floor(t*f+1e-9), g=Math.pow(b,compounds/f);\n let saved=0;\n for(let j=0;j!Number.isFinite(v)||v<0||v>max)||[annualRate,...(compare==='on'?[rateB]:[])].some(v=>!Number.isFinite(v)||v < -100||v>100))return{__error:'inputError'};\nconst a=project(principal,annualRate,years,deposit,depositFrequency,depositTiming);\nconst b=compare==='on'?project(principal,rateB,yearsB,depositB,depositFrequency,depositTiming):null;\nconst growth=[{period:0,contribution:principal,interest:0,balance:principal}];\nfor(let y=1;y0)growth.push({period:years,contribution:a.contribution,interest:a.interest,balance:a.amount});\nreturn{amount:a.amount,contribution:a.contribution,interest:a.interest,amountB:b?b.amount:null,contributionB:b?b.contribution:null,interestB:b?b.interest:null,balanceDifference:b?b.amount-a.amount:null,__growth:growth};", "inputs": [ { "name": "principal", "type": "number", "default": 10000, "min": 0, "step": 100, "max": 1000000000, "requiredValue": true, "strictRange": true }, { "name": "annualRate", "type": "number", "default": 7, "min": -100, "max": 100, "step": 0.01, "slider": true, "requiredValue": true, "strictRange": true }, { "name": "years", "type": "number", "default": 10, "min": 0, "max": 100, "step": 0.1, "slider": true, "requiredValue": true, "strictRange": true }, { "name": "compounds", "type": "select", "default": 12, "options": [ { "value": 1 }, { "value": 4 }, { "value": 12 }, { "value": 365 } ], "advanced": true }, { "name": "deposit", "type": "number", "default": 0, "min": 0, "max": 10000000, "step": 10, "requiredValue": true, "strictRange": true }, { "name": "depositFrequency", "type": "select", "default": 12, "options": [ { "value": 12 }, { "value": 1 } ] }, { "name": "depositTiming", "type": "select", "default": "end", "options": [ { "value": "end" }, { "value": "begin" } ], "advanced": true }, { "name": "compare", "type": "select", "default": "off", "options": [ { "value": "off" }, { "value": "on" } ] }, { "name": "depositB", "type": "number", "default": 100, "min": 0, "max": 10000000, "step": 10, "showWhen": { "compare": [ "on" ] }, "requiredValue": true, "strictRange": true }, { "name": "yearsB", "type": "number", "default": 10, "min": 0, "max": 100, "step": 0.1, "showWhen": { "compare": [ "on" ] }, "requiredValue": true, "strictRange": true }, { "name": "rateB", "type": "number", "default": 7, "min": -100, "max": 100, "step": 0.01, "showWhen": { "compare": [ "on" ] }, "requiredValue": true, "strictRange": true } ], "outputs": [ { "name": "amount", "precision": 2, "trimTrailingZeros": true }, { "name": "contribution", "precision": 2, "trimTrailingZeros": true }, { "name": "interest", "precision": 2, "trimTrailingZeros": true }, { "name": "amountB", "precision": 2, "optional": true, "trimTrailingZeros": true }, { "name": "contributionB", "precision": 2, "optional": true, "trimTrailingZeros": true }, { "name": "interestB", "precision": 2, "optional": true, "trimTrailingZeros": true }, { "name": "balanceDifference", "precision": 2, "optional": true, "trimTrailingZeros": true } ], "interpret": null } }