Calculating time to earn a specific amount as interest - python-3.x

Question

I cannot figure out the approach to this as the principle amount shall change after every year(if calculated annually, which shall be the easiest). Eventual goal is to calculate exact number of years, months and days to earn say 150000 as interest on a deposit of 1000000 at an interest rate of say 6.5%. I have tried but cannot seem to figure out how to increment the year/month/day in the loop. I don't mind if this is down voted because I have not posted any code(Well, they are wrong). This is not as simple as it might seem to beginners here.

Answer 1

It is a pure maths question. Compound interest is calculated as follows:
Ptotal = Pinitial*(1+rate/100)time
where Ptotal is the new total. rate is usually given in percentages so divide by 100; time is in years. You are interested in the difference, though, so use
interest = Pinitial*(1+rate/100)time – Pinitial
instead, which is in Python:
def compound_interest(P,rate,time):
interest = P*(1+rate/100)**time - P
return interest
A basic inversion of this to yield time, given P, r, and target instead, is
time = log((target+Pinitial)/Pinitial)/log(1+rate/100)
and this will immediately return the number of years. Converting the fraction to days is simple – an average year has 365.25 days – but for months you'll have to approximate.
At the bottom, the result is fed back into the standard compound interest formula to show it indeed returns the expected yield.
import math
def reverse_compound_interest(P,rate,target):
time = math.log((target+P)/P)/math.log(1+rate/100)
return time
timespan = reverse_compound_interest(2500000, 6.5, 400000)
print ('time in years',timespan)
years = math.floor(timespan)
months = math.floor(12*(timespan - years))
days = math.floor(365.25*(timespan - years - months/12))
print (years,'y',months,'m',days,'d')
print (compound_interest(2500000, 6.5, timespan))
will output
time in years 2.356815854829652
2 y 4 m 8 d
400000.0
Can we do better? Yes. datetime allows arbitrary numbers added to the current date, so assuming you start earning today (now), you can immediately get your date of $$$:
from datetime import datetime,timedelta
# ... original script here ...
timespan *= 31556926 # the number of seconds in a year
print ('time in seconds',timespan)
print (datetime.now() + timedelta(seconds=timespan))
which shows for me (your target date will differ):
time in years 2.356815854829652
time in seconds 74373863.52648607
2022-08-08 17:02:54.819492

Answer 2

You could do something like
def how_long_till_i_am_rich(investment, profit_goal, interest_rate):
profit = 0
days = 0
daily_interest = interest_rate / 100 / 365
while profit < profit_goal:
days += 1
profit += (investment + profit) * daily_interest
years = days // 365
months = days % 365 // 30
days = days - (months * 30) - (years * 365)
return years, months, days
years, months, days = how_long_till_i_am_rich(2500000, 400000, 8)
print(f"It would take {years} years, {months} months, and {days} days")
OUTPUT
It would take 1 years, 10 months, and 13 days