compound_interest

Calculate compound interest for investments or loans with various compounding frequencies, including annual, monthly, or continuous compounding.

Instructions

Calculate compound interest with various compounding frequencies.

Formulas: Discrete: A = P(1 + r/n)^(nt) Continuous: A = Pe^(rt)

Examples:

ANNUAL COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="annual" Result: £1628.89

MONTHLY COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="monthly" Result: £1647.01

CONTINUOUS COMPOUNDING: £1000 at 5% for 10 years principal=1000, rate=0.05, time=10, frequency="continuous" Result: £1648.72

Input Schema

TableJSON Schema

Name	Required	Description	Default
`context`	No	Optional annotation to label this calculation (e.g., 'Bond A PV', 'Q2 revenue'). Appears in results for easy identification.
`output_mode`	No	Output format: full (default), compact, minimal, value, or final. See batch_execute tool for details.	full
`principal`	Yes	Initial principal amount (e.g., 1000)
`rate`	Yes	Annual interest rate (e.g., 0.05 for 5%)
`time`	Yes	Time period in years (e.g., 10)
`frequency`	No	Compounding frequency	annual

Implementation Reference

src/vibe_math_mcp/tools/financial.py:306-347 (handler)

The main handler function implementing compound interest calculation using discrete or continuous compounding formulas based on principal, rate, time, and frequency.

async def compound_interest(
    principal: Annotated[float, Field(description="Initial principal amount (e.g., 1000)")],
    rate: Annotated[float, Field(description="Annual interest rate (e.g., 0.05 for 5%)")],
    time: Annotated[float, Field(description="Time period in years (e.g., 10)", ge=0)],
    frequency: Annotated[
        Literal["annual", "semi-annual", "quarterly", "monthly", "daily", "continuous"],
        Field(description="Compounding frequency"),
    ] = "annual",
) -> str:
    """Calculate compound interest."""
    try:
        freq_map = {
            "annual": 1,
            "semi-annual": 2,
            "quarterly": 4,
            "monthly": 12,
            "daily": 365,
        }

        if frequency == "continuous":
            # Continuous compounding: A = Pe^(rt)
            final_amount = principal * math.exp(rate * time)
        else:
            # Discrete compounding: A = P(1 + r/n)^(nt)
            n = freq_map[frequency]
            final_amount = principal * (1 + rate / n) ** (n * time)

        interest_earned = final_amount - principal

        return format_result(
            float(final_amount),
            {
                "principal": principal,
                "rate": rate,
                "time": time,
                "frequency": frequency,
                "interest_earned": float(interest_earned),
            },
        )
    except Exception as e:
        raise ValueError(f"Compound interest calculation failed: {str(e)}")

src/vibe_math_mcp/tools/financial.py:279-305 (registration)

The @mcp.tool decorator registering the compound_interest tool with name, description, examples, and annotations.

@mcp.tool(
    name="compound_interest",
    description="""Calculate compound interest with various compounding frequencies.

Formulas:
    Discrete: A = P(1 + r/n)^(nt)
    Continuous: A = Pe^(rt)

Examples:

ANNUAL COMPOUNDING: £1000 at 5% for 10 years
    principal=1000, rate=0.05, time=10, frequency="annual"
    Result: £1628.89

MONTHLY COMPOUNDING: £1000 at 5% for 10 years
    principal=1000, rate=0.05, time=10, frequency="monthly"
    Result: £1647.01

CONTINUOUS COMPOUNDING: £1000 at 5% for 10 years
    principal=1000, rate=0.05, time=10, frequency="continuous"
    Result: £1648.72""",
    annotations=ToolAnnotations(
        title="Compound Interest",
        readOnlyHint=True,
        idempotentHint=True,
    ),
)

src/vibe_math_mcp/tools/financial.py:307-314 (schema)

Pydantic schema definitions for the tool parameters including types, descriptions, constraints, and default value.

    principal: Annotated[float, Field(description="Initial principal amount (e.g., 1000)")],
    rate: Annotated[float, Field(description="Annual interest rate (e.g., 0.05 for 5%)")],
    time: Annotated[float, Field(description="Time period in years (e.g., 10)", ge=0)],
    frequency: Annotated[
        Literal["annual", "semi-annual", "quarterly", "monthly", "daily", "continuous"],
        Field(description="Compounding frequency"),
    ] = "annual",
) -> str:

src/vibe_math_mcp/tools/batch.py:14-21 (registration)

TOOL_CATEGORIES dictionary registering compound_interest under 'Financial' category for batch execution tool.

TOOL_CATEGORIES = {
    "Basic": ["calculate", "percentage", "round", "convert_units"],
    "Arrays": ["array_operations", "array_statistics", "array_aggregate", "array_transform"],
    "Statistics": ["statistics", "pivot_table", "correlation"],
    "Financial": ["financial_calcs", "compound_interest", "perpetuity"],
    "Linear Algebra": ["matrix_operations", "solve_linear_system", "matrix_decomposition"],
    "Calculus": ["derivative", "integral", "limits_series"],
}

Vibe Math MCP