curl --request POST \ --url https://api.iotools.cloud/v1/tool/rule-of-72-calculator \ --header 'Authorization: Bearer <token>' \ --header 'Content-Type: application/json' \ --data ' { "mode": "rate_to_years", "rate": "8", "frequency": "1" } '

{ "tool": "rule-of-72-calculator", "tool_version": "1.0.1", "outputs": { "summary": "=== Rule of 72 — Doubling Time ===\n\n At 8% per year, your money doubles in about 9.00 years (Rule of 72).\n The exact doubling time is 9.01 years — the rule is off by -0.07%.\n\n Annual Interest Rate: 8%\n Compounding: Annually (1x/year)\n\n Rule of 72: 9.00 years\n Rule of 70: 8.75 years\n Rule of 69.3: 8.66 years\n Exact (logarithmic): 9.01 years\n\n=== Formula ===\n Approximation: years ≈ 72 / rate\n Exact: years = ln(2) / ln(1 + rate/100)", "table": [ { "method": "Rule of 72", "result": "9.00 years", "error-vs-exact": "-0.07%", "best-for": "Most popular; most accurate for rates around 6-10%" }, { "method": "Rule of 70", "result": "8.75 years", "error-vs-exact": "-2.85%", "best-for": "Easier mental math; slight under-estimate at low rates" }, { "method": "Rule of 69.3", "result": "8.66 years", "error-vs-exact": "-3.82%", "best-for": "Closest to the true constant (69.3 ≈ 100·ln 2)" }, { "method": "Exact (logarithmic)", "result": "9.01 years", "error-vs-exact": "—", "best-for": "True value from the compound-interest formula" } ] }, "credits_used": 3, "credits_remaining": null }