Skip to content

Solver

collegeplan.solver

Required-savings solver using bisection root-finding.

solve_required_savings(children, assumptions, household_fund=None, target_funding_ratio=1.0, solve_mode='child_level', tolerance=1.0, max_iterations=100)

Find the annual contribution needed to reach a target funding ratio.

Parameters:

Name Type Description Default
children list[Child]

List of children to plan for.

 required
assumptions Assumptions

Return and inflation assumptions.

 required
household_fund HouseholdFund | None

Optional shared pool.

 None
target_funding_ratio float

Desired funding level (1.0 = fully funded).

 1.0
solve_mode str

"child_level" distributes contribution among children weighted by projected cost, "shared_pool" adds it to the household fund.

 'child_level'
tolerance float

Convergence tolerance in dollars.

 1.0
max_iterations int

Maximum bisection iterations.

 100
Source code in src/collegeplan/solver.py 
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
def solve_required_savings(
    children: list[Child],
    assumptions: Assumptions,
    household_fund: HouseholdFund | None = None,
    target_funding_ratio: float = 1.0,
    solve_mode: str = "child_level",
    tolerance: float = 1.0,
    max_iterations: int = 100,
) -> SavingsSolution:
    """Find the annual contribution needed to reach a target funding ratio.

    Args:
        children: List of children to plan for.
        assumptions: Return and inflation assumptions.
        household_fund: Optional shared pool.
        target_funding_ratio: Desired funding level (1.0 = fully funded).
        solve_mode: "child_level" distributes contribution among children
            weighted by projected cost, "shared_pool" adds it to the
            household fund.
        tolerance: Convergence tolerance in dollars.
        max_iterations: Maximum bisection iterations.
    """
    validate_plan(children, assumptions, household_fund)

    # Compute cost-based weights for child_level distribution
    weights = _cost_weights(children, assumptions) if solve_mode == "child_level" else None

    # Check if already funded with zero additional contribution
    current_ratio = _run_with_contribution(
        children, assumptions, household_fund, 0.0, solve_mode, weights
    )
    if current_ratio >= target_funding_ratio:
        return SavingsSolution(
            required_annual_contribution=0.0,
            required_monthly_contribution=0.0,
            per_child_suggestions={c.name: 0.0 for c in children},
            achieved_funding_ratio=current_ratio,
        )

    # Establish upper bound
    total_cost = sum(
        c.cost_profile.current_total_cost
        * (1 + c.cost_profile.annual_cost_growth) ** int(c.start_age - c.current_age)
        * c.attendance_years
        for c in children
    )
    min_years = max(1, min(int(c.start_age - c.current_age) for c in children))
    upper = total_cost / min_years

    # Verify upper bound is sufficient
    upper_ratio = _run_with_contribution(
        children, assumptions, household_fund, upper, solve_mode, weights
    )
    while upper_ratio < target_funding_ratio:
        upper *= 2
        upper_ratio = _run_with_contribution(
            children, assumptions, household_fund, upper, solve_mode, weights
        )
        if upper > total_cost * 10:
            raise SolverError("Cannot find a feasible contribution within reasonable bounds")

    # Bisection
    lo, hi = 0.0, upper
    for _ in range(max_iterations):
        mid = (lo + hi) / 2
        ratio = _run_with_contribution(
            children, assumptions, household_fund, mid, solve_mode, weights
        )
        if ratio < target_funding_ratio:
            lo = mid
        else:
            hi = mid
        if hi - lo < tolerance:
            break
    else:
        raise SolverError(f"Solver did not converge after {max_iterations} iterations")

    annual = (lo + hi) / 2
    monthly = annual / 12

    if weights is not None:
        per_child = {c.name: annual * weights[c.name] for c in children}
    else:
        n = len(children)
        per_child = {c.name: annual / n for c in children}

    # Verify achieved ratio
    achieved = _run_with_contribution(
        children, assumptions, household_fund, annual, solve_mode, weights
    )

    return SavingsSolution(
        required_annual_contribution=annual,
        required_monthly_contribution=monthly,
        per_child_suggestions=per_child,
        achieved_funding_ratio=achieved,
    )