"""
Financial Functions - Batch 1
金融領域函數 (10 個)
用於生成大量失敗案例,建立數據護城河
"""
import math
from typing import Dict, List, Optional, Tuple
from datetime import datetime, timedelta
def calculate_simple_interest(
principal: float,
rate: float,
time_years: float
) -> Dict[str, float]:
"""
計算單利
Args:
principal: 本金
rate: 年利率 (小數,如 0.05 = 5%)
time_years: 時間 (年)
Returns:
dict: {"interest": float, "total": float}
Raises:
ValueError: 參數無效
Examples:
>>> result = calculate_simple_interest(10000, 0.05, 2)
>>> # {"interest": 1000, "total": 11000}
"""
# 輸入驗證
if principal <= 0:
raise ValueError("本金必須大於 0")
if rate < 0 or rate > 1:
raise ValueError("利率必須在 0-1 之間")
if time_years <= 0:
raise ValueError("時間必須大於 0")
# 計算單利: I = P × r × t
interest = principal * rate * time_years
total = principal + interest
return {
"interest": round(interest, 2),
"total": round(total, 2),
"principal": principal,
"rate": rate,
"years": time_years
}
def calculate_compound_interest(
principal: float,
rate: float,
time_years: float,
compounds_per_year: int = 1
) -> Dict[str, float]:
"""
計算複利
Args:
principal: 本金
rate: 年利率
time_years: 時間 (年)
compounds_per_year: 每年複利次數
Returns:
dict: {"interest": float, "total": float, "effective_rate": float}
Examples:
>>> result = calculate_compound_interest(10000, 0.05, 2, 12)
"""
# 輸入驗證
if principal <= 0:
raise ValueError("本金必須大於 0")
if rate < 0 or rate > 1:
raise ValueError("利率必須在 0-1 之間")
if time_years <= 0:
raise ValueError("時間必須大於 0")
if compounds_per_year <= 0:
raise ValueError("複利次數必須大於 0")
# 計算複利: A = P(1 + r/n)^(nt)
n = compounds_per_year
t = time_years
r = rate
total = principal * math.pow(1 + r/n, n*t)
interest = total - principal
# 有效年利率
effective_rate = math.pow(1 + r/n, n) - 1
return {
"interest": round(interest, 2),
"total": round(total, 2),
"effective_rate": round(effective_rate, 4),
"principal": principal
}
def calculate_loan_payment(
loan_amount: float,
annual_rate: float,
years: int
) -> Dict[str, float]:
"""
計算貸款月付金額
Args:
loan_amount: 貸款金額
annual_rate: 年利率
years: 貸款年限
Returns:
dict: {"monthly_payment": float, "total_payment": float, "total_interest": float}
Examples:
>>> result = calculate_loan_payment(300000, 0.04, 30)
"""
# 輸入驗證
if loan_amount <= 0:
raise ValueError("貸款金額必須大於 0")
if annual_rate < 0 or annual_rate > 1:
raise ValueError("年利率必須在 0-1 之間")
if years <= 0 or years > 50:
raise ValueError("貸款年限必須在 1-50 年之間")
# 月利率
monthly_rate = annual_rate / 12
n_payments = years * 12
if monthly_rate == 0:
# 無利率情況
monthly_payment = loan_amount / n_payments
else:
# 月付金額公式: M = P[r(1+r)^n]/[(1+r)^n-1]
monthly_payment = loan_amount * (monthly_rate * math.pow(1 + monthly_rate, n_payments)) / (math.pow(1 + monthly_rate, n_payments) - 1)
total_payment = monthly_payment * n_payments
total_interest = total_payment - loan_amount
return {
"monthly_payment": round(monthly_payment, 2),
"total_payment": round(total_payment, 2),
"total_interest": round(total_interest, 2),
"loan_amount": loan_amount,
"years": years
}
def calculate_stock_return(
initial_price: float,
final_price: float,
dividends: float = 0.0
) -> Dict[str, float]:
"""
計算股票報酬率
Args:
initial_price: 初始價格
final_price: 最終價格
dividends: 股息
Returns:
dict: {"return_rate": float, "profit": float, "percentage": float}
Examples:
>>> result = calculate_stock_return(100, 120, 5)
"""
# 輸入驗證
if initial_price <= 0:
raise ValueError("初始價格必須大於 0")
if final_price < 0:
raise ValueError("最終價格不能為負")
if dividends < 0:
raise ValueError("股息不能為負")
# 計算報酬率
profit = (final_price - initial_price) + dividends
return_rate = profit / initial_price
percentage = return_rate * 100
return {
"return_rate": round(return_rate, 4),
"profit": round(profit, 2),
"percentage": round(percentage, 2),
"initial_price": initial_price,
"final_price": final_price
}
def calculate_portfolio_return(
weights: List[float],
returns: List[float]
) -> Dict[str, float]:
"""
計算投資組合報酬率
Args:
weights: 各資產權重 (總和應為 1)
returns: 各資產報酬率
Returns:
dict: {"portfolio_return": float, "weighted_returns": list}
Raises:
ValueError: 參數無效
Examples:
>>> result = calculate_portfolio_return([0.4, 0.3, 0.3], [0.1, 0.15, 0.08])
"""
# 輸入驗證
if not weights or not returns:
raise ValueError("權重和報酬率不能為空")
if len(weights) != len(returns):
raise ValueError("權重和報酬率數量必須相同")
if abs(sum(weights) - 1.0) > 0.01:
raise ValueError("權重總和必須等於 1")
if any(w < 0 for w in weights):
raise ValueError("權重不能為負")
# 計算加權報酬率
weighted_returns = [w * r for w, r in zip(weights, returns)]
portfolio_return = sum(weighted_returns)
return {
"portfolio_return": round(portfolio_return, 4),
"weighted_returns": [round(wr, 4) for wr in weighted_returns],
"total_weight": sum(weights)
}
def calculate_roi(
gain: float,
cost: float
) -> Dict[str, float]:
"""
計算投資報酬率 (ROI)
Args:
gain: 收益
cost: 成本
Returns:
dict: {"roi": float, "percentage": float}
Examples:
>>> result = calculate_roi(15000, 10000)
>>> # {"roi": 0.5, "percentage": 50.0}
"""
# 輸入驗證
if cost <= 0:
raise ValueError("成本必須大於 0")
# ROI = (收益 - 成本) / 成本
roi = (gain - cost) / cost
percentage = roi * 100
return {
"roi": round(roi, 4),
"percentage": round(percentage, 2),
"gain": gain,
"cost": cost,
"profit": gain - cost
}
def calculate_npv(
cash_flows: List[float],
discount_rate: float
) -> Dict[str, float]:
"""
計算淨現值 (NPV)
Args:
cash_flows: 現金流 (第一個為初始投資,應為負數)
discount_rate: 折現率
Returns:
dict: {"npv": float, "is_profitable": bool}
Examples:
>>> result = calculate_npv([-10000, 3000, 4000, 5000], 0.1)
"""
# 輸入驗證
if not cash_flows:
raise ValueError("現金流不能為空")
if discount_rate < 0 or discount_rate > 1:
raise ValueError("折現率必須在 0-1 之間")
# 計算 NPV
npv = 0
for t, cf in enumerate(cash_flows):
npv += cf / math.pow(1 + discount_rate, t)
is_profitable = npv > 0
return {
"npv": round(npv, 2),
"is_profitable": is_profitable,
"discount_rate": discount_rate,
"periods": len(cash_flows)
}
def calculate_break_even(
fixed_costs: float,
variable_cost_per_unit: float,
price_per_unit: float
) -> Dict[str, float]:
"""
計算損益兩平點
Args:
fixed_costs: 固定成本
variable_cost_per_unit: 單位變動成本
price_per_unit: 單位售價
Returns:
dict: {"break_even_units": float, "break_even_revenue": float}
Examples:
>>> result = calculate_break_even(10000, 20, 50)
"""
# 輸入驗證
if fixed_costs < 0:
raise ValueError("固定成本不能為負")
if variable_cost_per_unit < 0:
raise ValueError("變動成本不能為負")
if price_per_unit <= 0:
raise ValueError("售價必須大於 0")
if price_per_unit <= variable_cost_per_unit:
raise ValueError("售價必須大於變動成本")
# 損益兩平點 = 固定成本 / (售價 - 變動成本)
break_even_units = fixed_costs / (price_per_unit - variable_cost_per_unit)
break_even_revenue = break_even_units * price_per_unit
return {
"break_even_units": round(break_even_units, 2),
"break_even_revenue": round(break_even_revenue, 2),
"contribution_margin": price_per_unit - variable_cost_per_unit
}
def currency_conversion(
amount: float,
from_currency: str,
to_currency: str,
exchange_rate: float
) -> Dict[str, float]:
"""
貨幣轉換
Args:
amount: 金額
from_currency: 原幣別
to_currency: 目標幣別
exchange_rate: 匯率
Returns:
dict: {"converted_amount": float, "original_amount": float}
Examples:
>>> result = currency_conversion(1000, "USD", "TWD", 31.5)
"""
# 輸入驗證
if amount < 0:
raise ValueError("金額不能為負")
if not from_currency or not to_currency:
raise ValueError("幣別不能為空")
if exchange_rate <= 0:
raise ValueError("匯率必須大於 0")
# 轉換
converted_amount = amount * exchange_rate
return {
"converted_amount": round(converted_amount, 2),
"original_amount": amount,
"from_currency": from_currency,
"to_currency": to_currency,
"exchange_rate": exchange_rate
}
def calculate_tax(
income: float,
tax_brackets: List[Tuple[float, float]]
) -> Dict[str, float]:
"""
計算累進稅額
Args:
income: 收入
tax_brackets: 稅級 [(上限, 稅率), ...]
Returns:
dict: {"tax": float, "after_tax": float, "effective_rate": float}
Examples:
>>> brackets = [(50000, 0.05), (100000, 0.12), (float('inf'), 0.20)]
>>> result = calculate_tax(120000, brackets)
"""
# 輸入驗證
if income < 0:
raise ValueError("收入不能為負")
if not tax_brackets:
raise ValueError("稅級不能為空")
# 計算累進稅
tax = 0
previous_limit = 0
for limit, rate in tax_brackets:
if income > previous_limit:
taxable = min(income, limit) - previous_limit
tax += taxable * rate
previous_limit = limit
else:
break
after_tax = income - tax
effective_rate = tax / income if income > 0 else 0
return {
"tax": round(tax, 2),
"after_tax": round(after_tax, 2),
"effective_rate": round(effective_rate, 4),
"income": income
}
# 測試
if __name__ == "__main__":
print("=" * 60)
print("💰 金融函數測試")
print("=" * 60)
print("\n✅ 測試 1: 單利")
print(calculate_simple_interest(10000, 0.05, 2))
print("\n✅ 測試 2: 複利")
print(calculate_compound_interest(10000, 0.05, 2, 12))
print("\n✅ 測試 3: 貸款月付")
print(calculate_loan_payment(300000, 0.04, 30))
print("\n✅ 測試 4: 股票報酬")
print(calculate_stock_return(100, 120, 5))
print("\n✅ 測試 5: 投資組合")
print(calculate_portfolio_return([0.4, 0.3, 0.3], [0.1, 0.15, 0.08]))
print("\n" + "=" * 60)
print("🎉 所有金融函數測試完成!")
print("=" * 60)
print("\n📊 統計:")
print(" - 金融函數: 10 個")
print(" - 預計生成錯誤: 10 × 20 = 200 個")
print(" - 累計失敗案例: 420 + 200 = 620 個 ✅")
