Calculate how much money to deposit in a fixed deposit account in order to earn the maximum amount of interest after rounding up or down.

rate.py

import math


def actual_final(month, rate, save):
    current = save
    for _ in range(month):
        current = round(current * (1 + rate / 100 / 12))
    return current


def ideal_final(month, rate, save):
    return save * (1 + rate / 100 / 12)**month


def get_most_money(month, rate, start, end):
    cur_max = -math.inf
    best_begin = None
    best_final = None
    for save in range(start, end):
        actual = actual_final(month, rate, save)
        ideal = ideal_final(month, rate, save)
        diff = actual - ideal
        if diff > cur_max:
            cur_max = diff
            best_begin = save
            best_final = actual
    print(f'Save {best_begin} will get more {cur_max} and total {best_final}')


get_most_money(12, 1.58, 8000, 15000)
get_most_money(12, 1.58, 25000, 35000)
get_most_money(12, 1.58, 45000, 55000)
get_most_money(12, 1.58, 65000, 75000)
get_most_money(12, 1.58, 85000, 95000)
get_most_money(12, 1.58, 105000, 115000)
get_most_money(12, 1.58, 135000, 141000)
get_most_money(12, 1.58, 1, 2000000)

# Save 8735 will get more 4.983156386773771 and total 8879
# Save 25444 will get more 3.06072479737486 and total 25852
# Save 54344 will get more 1.1194791852103663 and total 55210
# Save 71773 will get more 1.738303760488634 and total 72917
# Save 85444 will get more 1.1654051873483695 and total 86805
# Save 114309 will get more 1.7811818449554266 and total 116130
# Save 140914 will get more 1.3646822078735568 and total 143158

# Save 380 will get more 5.952329642469863 and total 392