{"id":"rate-nominal-effective-convert","version":"1.0.0","description":"Convert an interest rate between nominal (periodic compounding), effective annual and continuous compounding forms.","supported_operations":["nominal to effective annual rate","APR to APY conversion","effective annual rate from stated rate","convert monthly compounded rate to annual effective","continuous compounding rate equivalent","effective rate to nominal rate","compare rates with different compounding","EAR of a nominal rate compounded quarterly","המרת ריבית נומינלית לריבית אפקטיבית שנתית"],"unsupported_operations":["solving a rate from a payment stream, fees or a loan (use loan-apr-compute)","accruing interest on an amount over a term (use interest-accrual-compute)","inflation adjustment or real rates","percent-formatted input such as \"5%\""],"semantics":["rate is a decimal fraction string (0.08 means 8 percent; \"8\" means 800 percent) with -1 < rate <= 10, at most 20 integer and 20 fractional digits. A JSON number, percent sign or exponent form is invalid_input.","from_compounding says what rate means: an integer m from 1 to 365 (a nominal annual rate compounded m times a year), \"continuous\", or \"effective\" (an effective annual rate, the same as m = 1). to_compounding takes the same values and names the requested form; both are required.","The conversion goes through the exact effective annual rate: EAR = (1 + rate/m)^m - 1 for integer m (exact rational arithmetic), e^rate - 1 for continuous, rate for effective. Target form: m * ((1 + EAR)^(1/m) - 1) for integer m, ln(1 + EAR) for continuous, EAR for effective.","Outputs: rate (in the to_compounding form), effective_annual_rate (EAR) and continuous_rate (ln(1 + EAR), 0 when EAR is 0), each rounded once from the exact value to rate_scale fractional digits. Same-form conversions return the input rounded exactly. Defaults when omitted: rate_scale 10, rounding half-up (half away from zero); the other modes are half-even, half-down, up, down, ceiling, floor. Outputs never contain -0.","Roots, exponentials and logarithms use a 40-digit BigInt engine accurate to better than 1e-35 relative before the final rounding.","Any string input over 64 UTF-8 bytes is limit_exceeded, checked before parsing; a lone surrogate is invalid_input.","Disclaimer: arithmetic calculation only; not financial, tax, legal, or investment advice."],"limits":{"max_string_bytes":64},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["rate","from_compounding","to_compounding"],"properties":{"rate":{"type":"string","pattern":"^-?(0|[1-9][0-9]*)(\\.[0-9]+)?$","maxLength":64},"from_compounding":{"oneOf":[{"type":"integer","minimum":1,"maximum":365},{"type":"string","enum":["continuous","effective"]}]},"to_compounding":{"oneOf":[{"type":"integer","minimum":1,"maximum":365},{"type":"string","enum":["continuous","effective"]}]},"rate_scale":{"type":"integer","minimum":0,"maximum":12},"rounding":{"type":"string","enum":["half-up","half-even","half-down","up","down","ceiling","floor"]}}},"output_schema":{"type":"object","additionalProperties":false,"required":["rate","effective_annual_rate","continuous_rate"],"properties":{"rate":{"type":"string","pattern":"^-?(0|[1-9][0-9]*)(\\.[0-9]+)?$","maxLength":64},"effective_annual_rate":{"type":"string","pattern":"^-?(0|[1-9][0-9]*)(\\.[0-9]+)?$","maxLength":64},"continuous_rate":{"type":"string","pattern":"^-?(0|[1-9][0-9]*)(\\.[0-9]+)?$","maxLength":64}}},"examples":[{"input":{"rate":"0.0525","from_compounding":4,"to_compounding":"effective","rate_scale":6},"output":{"rate":"0.053543","effective_annual_rate":"0.053543","continuous_rate":"0.052158"}},{"input":{"rate":"0.053543","from_compounding":"effective","to_compounding":4,"rate_scale":6},"output":{"rate":"0.052500","effective_annual_rate":"0.053543","continuous_rate":"0.052159"}},{"input":{"rate":"0.08","from_compounding":"continuous","to_compounding":12,"rate_scale":8},"output":{"rate":"0.08026726","effective_annual_rate":"0.08328707","continuous_rate":"0.08000000"}}],"execute_url":"/v1/tools/rate-nominal-effective-convert/versions/1.0.0/execute"}