Python - Accumulated Value of Annual Investment

Question

I have a program (futval.py) that will calculate the value of an investment after 10 years. I want to modify the program so that instead of calculating the value of a one time investment after 10 years, it will calculate the value of an annual investment after 10 years. I want to do this without using an accumulator variable. Is it possible to do this with only the variables that were present in the original program (investment, apr, i)?

# 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()

I was not able to accomplish modifying the program without introducing the 'futval' accumulator variable.

# 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()

It's a problem in a Python textbook I'm using. Supposedly, it's possible to do it without introducing an accumulator variable, but I can't figure out how. — TexanBruceWayne, Jul 08 '16 at 21:34
I'm pretty sure it would be futval = (investment*10)((1+apr)**10) — Natecat, Jul 08 '16 at 21:43
@Natecat This would be right if only he invested 10 times in the beginning of the very first year. — Vsevolod Timchenko, Jul 08 '16 at 23:14

Vsevolod Timchenko · Answer 1 · 2016-07-08T23:10:24.177

Okay, if you try doing some math you will see the solution yourself. For the first year we have:

new_value = investment*(1 + apr)

For the second:

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

or

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

Et cetera. If you actually try multiplying this stuff, you'll see that after 10 years the final value is

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

so the solution for your problem is just

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

EDIT: Somehow I managed to overlook the fact that what I wrote is just a geometric series, so the answer is even simpler:

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

score 0 · Answer 2 · answered Jul 08 '16 at 23:18

Well, you don't need an accumulator, but you still need a temporary variable to hold the original value of the periodic investment:

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: ")

    hold = investment
    investment = investment / apr

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

    investment = investment - hold / apr

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

main()

So the guy asks "Is it possible to do this with only the variables that were present in the original program (investment, apr, i)?" and your answer is "Add an additional variable"? That's... bold. — Vsevolod Timchenko, Jul 08 '16 at 23:26

Python - Accumulated Value of Annual Investment

2 Answers2