Python——年度投资累计值

Question

我有一个程序 (futval.py)，可以计算 10 年后的投资值(value)。我想修改程序，使其不再计算10年后的一次性投资的值(value)，而是计算10年后每年投资的值(value)。我想在不使用累加器变量的情况下执行此操作。是否可以仅使用原始程序中存在的变量(投资、年利率、i)来执行此操作？

# futval.py
# A program to compute the value of an investment
# carried 10 years into the future

def main():
    print "This program calculates the future value",
    print "of a 10-year investment."

    investment = input("Enter the initial investment: ")
    apr = input("Enter the annual interest rate: ")

    for i in range(10):
        investment = investment * (1 + apr)

    print "The value in 10 years is:", investment

main()

如果不引入“futval”累加器变量，我无法完成程序修改。

# futval10.py
# A program to compute the value of an annual investment
# carried 10 years into the future

def main():
    print "This program calculates the future value",
    print "of a 10-year annual investment."

    investment = input("Enter the annual investment: ")
    apr = input("Enter the annual interest rate: ")

    futval = 0

    for i in range(10):
        futval = (futval + investment) * (1+apr)

    print "The value in 10 years is:", futval

main()

Answer 1

好吧，如果你尝试做一些数学计算，你就会自己找到解决方案。第一年我们有:

new_value = investment*(1 + apr)

对于第二个:

new_second_value = (new_value + investment)*(1+apr)

或

new_second_value = (investment*(1 + apr) + investment)*(1+apr)

等等。如果你真的尝试将这些东西相乘，你会发现 10 年后的最终值是

investment*((1+apr)**10) + investment*((1+apr)**9)+...   etc

所以你的问题的解决方案就是

print("The value in 10 years is:", sum([investment*((1+apr)**i) for i in range(1, 11)]))

编辑:不知怎的，我设法忽略了这样一个事实:我写的只是一个几何级数，所以答案更简单:

ten_years_annual_investment = investment*(apr+1)*((apr+1)**10 - 1)/apr