量化：年化收益、期初收益、期末收益、年份，任意3个值计算剩下的1个值

1
网页计算器可以参考：（新浪财经投资收益计算器）http://finance.sina.com.cn/money/283/2005/0708/19.html

计算方法

由图可知：

F V = ( 1 + r ) n ∗ P V FV=(1+r)^n * PV FV=(1+r)n∗PV

其中：

• FV：初始值
• PV：终值

由此计算，可知：

1. P V = F V ( 1 + r ) n PV = \frac{FV}{(1+r)^n} PV=(1+r)nFV​
2. n = log ⁡ ( 1 + r ) F V P V n=\log_{(1+r)}{\frac{FV}{PV} } n=log(1+r)​PVFV​
3. r = F V P V n − 1 r = \sqrt[n]{\frac{FV}{PV} } -1 r=nPVFV​ ​−1

python的计算方法如下：

计算函数&代码

import numpy as np


def cal_annualized_income(start_value=0, end_value=0, years=0, annualized=0.0):
    """
    计算年化收益、期初收益、期末收益
    :param start_value: 期初资产
    :param end_value: 期末资产
    :param years: 时间(年)
    :param annualized: 年化收益率
    :return:
    """
    if end_value and years and annualized:  # 计算初始值 start_value
        start_value = end_value / np.power(1 + annualized, years)
        return start_value
    if start_value and years and annualized:  # 计算终值 end_value
        end_value = start_value * np.power(1 + annualized, years)
        return end_value
    if start_value and end_value and annualized:  # 计算年限 years
        years = - np.log(end_value / start_value) / np.log(1 / (1 + annualized))
        return round(years, 2)
    if start_value and end_value and years:  # 计算年化收益率 annualized
        annualized = np.power(end_value / start_value, 1 / years) - 1
        return annualized


def main():
    annual_value = cal_annualized_income(start_value=100, end_value=500, years=10)  # 计算收益率
    end_value = cal_annualized_income(start_value=100, years=10, annualized=0.05)  # 计算终值
    year_value = cal_annualized_income(start_value=100, end_value=600, annualized=0.06)  # 计算年份
    start_value = cal_annualized_income(end_value=500, years=10, annualized=0.05)  # 期初资产


if __name__ == '__main__':
    main()