import matplotlib.pyplot as plt
import numpy as np
 
# 設定中文字型與風格 (使用內建字型以確保顯示)
plt.rcParams['font.sans-serif'] = ['Taipei Sans TC Beta', 'Microsoft JhengHei', 'SimHei', 'Arial']
plt.rcParams['axes.unicode_minus'] = False
plt.style.use('seaborn-v0_8-whitegrid')
 
# 模擬參數
np.random.seed(101) # 固定種子以求結果一致
n_simulations = 5000 
mu = 0.075   # 7.5%
sigma = 0.16 # 16%
initial_principal = 100
contribution_amount = 80
 
def run_simulation(years, contributions):
    sim_paths = np.zeros((n_simulations, years + 1))
    sim_paths[:, 0] = initial_principal
    cost_line = np.zeros(years + 1)
    cost_line[0] = initial_principal
 
    for t in range(1, years + 1):
        shock = np.random.normal(0, 1, n_simulations)
        returns = np.exp((mu - 0.5 * sigma**2) + sigma * shock)
        sim_paths[:, t] = sim_paths[:, t-1] * returns
        cost_line[t] = cost_line[t-1]
 
        if t in contributions:
             sim_paths[:, t] += contribution_amount
             cost_line[t] += contribution_amount
    return sim_paths, cost_line
 
def plot_chart(years, contributions, title, filename):
    sim_paths, cost_line = run_simulation(years, contributions)
 
    p10 = np.percentile(sim_paths, 10, axis=0)
    p50 = np.percentile(sim_paths, 50, axis=0)
    p90 = np.percentile(sim_paths, 90, axis=0)
 
    # 設定高解析度畫布
    fig, ax = plt.subplots(figsize=(12, 7), dpi=300)
 
    x = np.arange(0, years + 1)
 
    # 繪製區域
    ax.fill_between(x, p10, p90, color='#87CEEB', alpha=0.4, label='80% 機率分佈 (P10-P90)')
 
    # 繪製線條
    ax.plot(x, p50, color='#00008B', linewidth=3, label='中位數 (P50) - 最可能的結果')
    ax.step(x, cost_line, color='#DC143C', linestyle='--', linewidth=2.5, where='post', label='投入本金 (成本)')
 
    # 標示數值
    ax.text(years, p90[-1], f' P90 (樂觀): {int(p90[-1])}', fontsize=12, color='#00008B', fontweight='bold', va='center')
    ax.text(years, p50[-1], f' P50 (中位): {int(p50[-1])}', fontsize=12, color='#00008B', fontweight='bold', va='center')
    ax.text(years, p10[-1], f' P10 (悲觀): {int(p10[-1])}', fontsize=12, color='#00008B', fontweight='bold', va='top')
    ax.text(years, cost_line[-1], f' 總成本: {int(cost_line[-1])}', fontsize=12, color='#DC143C', fontweight='bold', va='top')
 
    # 標題與標籤
    ax.set_title(title, fontsize=18, fontweight='bold', pad=20)
    ax.set_xlabel('年份 (Year)', fontsize=14)
    ax.set_ylabel('資產金額 (Value)', fontsize=14)
    ax.set_xlim(0, years + 1)
    ax.grid(True, linestyle='--', alpha=0.6)
    ax.legend(loc='upper left', fontsize=12, frameon=True, facecolor='white', framealpha=0.9)
 
    plt.tight_layout()
    plt.show()
 
# 執行繪圖
plot_chart(10, [1, 4, 7], "情境一：10年期 (第1,4,7年加碼)", "chart1")
plot_chart(13, [1, 4, 7, 10], "情境二：13年期 (第1,4,7,10年加碼)", "chart2")
plot_chart(16, [1, 4, 7, 10, 13], "情境三：16年期 (第1,4,7,10,13年加碼)", "chart3")
 

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