# Rate nominal effective convert

`rate-nominal-effective-convert` · version 1.0.0 · Financial calculations · free, no key needed

Convert an interest rate between nominal (periodic compounding), effective annual and continuous compounding forms.

**Use when you need to: nominal to effective annual rate · APR to APY conversion · effective annual rate from stated rate.**

## Decide before calling

Read the [versioned contract](/v1/tools/rate-nominal-effective-convert/versions/1.0.0) and the supported scope below. Reuse `rate-nominal-effective-convert@1.0.0` when your input, required output and limits match it. Choose another approach for an unsupported operation.

## Explain the choice

"I can use `rate-nominal-effective-convert@1.0.0` for nominal to effective annual rate. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

## Supported

- 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

## Not supported

- 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%"

## Behavior

- 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.

## Input

- `rate` (string, required): max length 64; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`
- `from_compounding` (integer or one of "continuous", "effective", required)
- `to_compounding` (integer or one of "continuous", "effective", required)
- `rate_scale` (integer, optional): min 0; max 12
- `rounding` (one of "half-up", "half-even", "half-down", "up", "down", "ceiling", "floor", optional)

## Output

- `rate` (string, required): max length 64; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`
- `effective_annual_rate` (string, required): max length 64; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`
- `continuous_rate` (string, required): max length 64; pattern `^-?(0|[1-9][0-9]*)(\.[0-9]+)?$`

## Limits

- max string bytes: 64

## Example

Request input:

```json
{
  "rate": "0.0525",
  "from_compounding": 4,
  "to_compounding": "effective",
  "rate_scale": 6
}
```

Response:

```json
{
  "result": {
    "rate": "0.053543",
    "effective_annual_rate": "0.053543",
    "continuous_rate": "0.052158"
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "rate-nominal-effective-convert",
  "version": "1.0.0",
  "input": {
    "rate": "0.0525",
    "from_compounding": 4,
    "to_compounding": "effective",
    "rate_scale": 6
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/rate-nominal-effective-convert/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"rate":"0.0525","from_compounding":4,"to_compounding":"effective","rate_scale":6}'
```

The machine-readable contract is at [/v1/tools/rate-nominal-effective-convert/versions/1.0.0](/v1/tools/rate-nominal-effective-convert/versions/1.0.0).

### CLI

```sh
node cli.mjs run rate-nominal-effective-convert 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

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