# Compound interest with deposits in Python

I am working on an assignment for a comp sci class. I feel like I am really close but I cant quite get to the answer. Basically the assignment is a compound interest calculator, what I am trying to do that makes it more complicated is adding deposits to the initial investment and allowing for someone to stop paying into it at one point, but collect it at a different point. The example is ", a user may already have saved $10,000 in their account when they start their retirement calculation. They intend to save another $1000 per year for the next 10 years at which point they will stop making any additional deposits into their account. However, they may be 20 years away from retirement. Your program should be able to account for these varying inputs and calculate the correct future value of their account at retirement"

Here is my code so far:

def main(): print("Welcome to Letmeretire.com's financial retirement calculator!") import random num = random.randrange(10000) principal = int(input("How much are you starting with for your retirement savings?")) deposit = int(input("How much money do you plan to deposit each year?")) interest = int(input("How much interest will your account accrue annually")) time = int(input("Please enter the number of years that you plan to deposit money for.")) time_till_retirement = int(input("How long until you plan on retiring? (Please enter this amount in years)")) t = time + 1 APR = interest/100 R = ((1+APR/12)**12)-1 DR = deposit/R DRT = deposit/(R*(1+R)**time) PV = principal+(DR-DRT) future_value = PV*((1+APR/12)**12*time) if time < time_till_retirement: time1 = (time_till_retirement-time) future = future_value*((1+APR/12)**12*time1) else: future = future_value for i in range(1, t): print("After " + str(i) + " years you will have "+ str(future) + " saved!") main()

I would like the output to look like this:

Enter annual deposit: 1000 Enter interest rate: 12 Enter number of years until retirement: 10 What's the current balance of your account: 5000 How many years will you make your annual deposit? 5 After 1 year, you have: $ 6720.0 After 2 years, you have: $ 8646.4 After 3 years, you have: $ 10803.97 After 4 years, you have: $ 13220.44 After 5 years, you have: $ 15926.9 After 6 years, you have: $ 17838.13 After 7 years, you have: $ 19978.7 After 8 years, you have: $ 22376.14 After 9 years, you have: $ 25061.28 After 10 years, you have: $ 28068.64 But what Im getting is this: Welcome to Letmeretire.com's financial retirement calculator! How much are you starting with for your retirement savings?5000 How much money do you plan to deposit each year?1000 How much interest will your account accrue annually12 Please enter the number of years that you plan to deposit money for.5 How long until you plan on retiring? (Please enter this amount in years)10 After 1 years you will have 271235.9643776919 saved! After 2 years you will have 271235.9643776919 saved! After 3 years you will have 271235.9643776919 saved! After 4 years you will have 271235.9643776919 saved! After 5 years you will have 271235.9643776919 saved!

## Answers

I think you need to ensure the formula is correct:

FV(t) = 5000 * (1.12 ** t) + 1000 * (1.12 ** t) + 1000 * (1.12 ** (t-1)) + ... + 1000 * 1.12 = 5000 * (1.12 ** t) + 1000 * (1.12 ** t - 1) * 1.12 / 0.12

Then we can define a function:

def fv(t, initial, annual, interest_rate): return initial * (1+interest_rate) ** t + \ annual * (1+interest_rate) * ((1+interest_rate) ** t - 1) / interest_rate

Test:

print fv(1, 5000, 1000, 0.12) print fv(3, 5000, 1000, 0.12) print fv(5, 5000, 1000, 0.12)

Yields:

6720.0 10803.968 15926.8974592

Till now the main work is done, I think you can handle the rest.

In most cases, I would prefer Ray's analytic solution - plug the values into a formula, get the final answer, instead of iterating year by year.

However, in this case, you *want* the values for each year, so you may as well iterate after all:

import sys # Python 2/3 compatibility shim if sys.hexversion < 0x3000000: rng = xrange inp = raw_input else: rng = range inp = input def getter_fn(datatype): if datatype == str: return inp else: def fn(prompt=''): while True: try: return datatype(inp(prompt)) except ValueError: pass return fn get_float = getter_fn(float) get_int = getter_fn(int) def main(): print("Welcome to Letmeretire.com's financial retirement calculator!") principal = get_float("Initial investment amount? ") periods = get_int ("How many years will you make an annual deposit? ") deposit = get_float("Annual deposit amount? ") apr = get_float("Annual interest rate (in percent)? ") / 100 retirement = get_int ("Years until retirement? ") deposits = [deposit] * periods no_deposits = [0.] * (retirement - periods) amount = principal for yr, d in enumerate(deposits + no_deposits, 1): amount = (amount + d) * (1. + apr) print('After {:>2d} year{} you have: $ {:>10.2f}'.format(yr, 's,' if yr > 1 else ', ', amount)) if __name__ == '__main__': main()

which results in

Welcome to the Letmeretire.com financial retirement calculator! Initial investment amount? 5000 How many years will you make an annual deposit? 5 Annual deposit amount? 1000 Annual interest rate (in percent)? 12 Years until retirement? 10 After 1 year, you have: $ 6720.00 After 2 years, you have: $ 8646.40 After 3 years, you have: $ 10803.97 After 4 years, you have: $ 13220.44 After 5 years, you have: $ 15926.90 After 6 years, you have: $ 17838.13 After 7 years, you have: $ 19978.70 After 8 years, you have: $ 22376.14 After 9 years, you have: $ 25061.28 After 10 years, you have: $ 28068.64

FV(t) = 5000 * (1.12 ** t) + 1000 * (1.12 ** t) + 1000 * (1.12 ** (t-1)) + ... + 1000 * 1.12 = 5000 * (1.12 ** t) + 1000 * (1.12 ** t - 1) * 1.12 / 0.12

I have a similar problem like the one mentioned above but I do not get why the second part of the equation(formula) after the second equal sign? Also is there not another way of doing this more concise without having to code "FV(t) = 5000 * (1.12 ** t) + 1000 * (1.12 ** t) + 1000 * (1.12 ** (t-1))" this part several times?