Code Fights - depositProfit

README.md

You have deposited a specific amount of dollars into your bank account. Each year your balance increases at the same growth rate. Find out how long it would take for your balance to pass a specific threshold with the assumption that you don't make any additional deposits.

Example

For deposit = 100, rate = 20 and threshold = 170, the output should be
depositProfit(deposit, rate, threshold) = 3.

Each year the amount of money on your account increases by 20%. It means that throughout the years your balance would be:

• year 0: 100;
• year 1: 120;
• year 2: 144;
• year 3: 172,8.

Thus, it will take 3 years for your balance to pass the threshold, which is the answer.

Input/Output

• [time limit] 4000ms (py3)

• [input] integer deposit

  The initial deposit as a positive integer.

  Guaranteed constraints:

  1 ≤ deposit ≤ 100.
  

• [input] integer rate

  The rate of increase. Each year the balance increases by the rate percent of the current sum.

  Guaranteed constraints:

  1 ≤ rate ≤ 100.
  

• [input] integer threshold

  The target balance.

  Guaranteed constraints:

  deposit < threshold ≤ 200.
  

• [output] integer

  The number of years it would take to hit the threshold.

deposit_profit.py

import math


def deposit_profit(deposit, rate, threshold):
    return math.ceil((math.log(threshold) - math.log(deposit))/(math.log(1 + (rate / 100))))

test_deposit_profit.py

import unittest
from deposit_profit import deposit_profit


class TestDepositProfit(unittest.TestCase):
    def test_1(self):
        deposit = 100
        rate = 20
        threshold = 170
        solution = 3
        result = deposit_profit(deposit, rate, threshold)
        self.assertEqual(result, solution)

    def test_2(self):
        deposit = 100
        rate = 1
        threshold = 101
        solution = 1
        result = deposit_profit(deposit, rate, threshold)
        self.assertEqual(result, solution)

    def test_3(self):
        deposit = 1
        rate = 100
        threshold = 64
        solution = 6
        result = deposit_profit(deposit, rate, threshold)
        self.assertEqual(result, solution)


if __name__ == '__main__':
    unittest.main()