With compound interest, the interest for each year is added to the balance, and next year's interest is calculated on that larger balance. The amount after t years is A = P × (1 + r / 100)^t, where P is the principal and r is the yearly rate in percent.
The program
python
principal = float(input("Principal: ")) rate = float(input("Rate per year (%): ")) years = int(input("Time (years): ")) amount = principal * (1 + rate / 100) ** years interest = amount - principal print(f"Amount after {years} years = {amount:.2f}") print(f"Compound interest = {interest:.2f}")
Typed in this example: 10000, 7.5, 3. Press Run to type your own.
output
Principal: 10000 Rate per year (%): 7.5 Time (years): 3 Amount after 3 years = 12422.97 Compound interest = 2422.97
How it works
1 + rate / 100is the growth factor for one year: 1.075 for 7.5%.** yearsmultiplies by that factor once for each year.- With simple interest, the same numbers give 2250.00. Compound interest gives 172.97 more, because years 2 and 3 also earn interest on the earlier interest.
Year by year
A loop shows the same result one year at a time:
python
principal = 10000 rate = 7.5 balance = principal for year in range(1, 4): interest = balance * rate / 100 balance += interest print(f"Year {year}: interest {interest:8.2f}, balance {balance:9.2f}")
output
Year 1: interest 750.00, balance 10750.00 Year 2: interest 806.25, balance 11556.25 Year 3: interest 866.72, balance 12422.97
The interest grows every year, because the balance it is calculated on grows.
Compounding n times per year
Many banks add interest monthly or daily instead of once a year. With n periods per year, each period uses the rate divided by n, and there are n * years periods: A = P × (1 + r / (100 × n))^(n × t).
python
principal = 10000 rate = 7.5 years = 3 for name, n in [("yearly", 1), ("half-yearly", 2), ("quarterly", 4), ("monthly", 12), ("daily", 365)]: amount = principal * (1 + rate / 100 / n) ** (n * years) print(f"{name:<12} {amount:9.2f}")
output
yearly 12422.97 half-yearly 12471.79 quarterly 12497.16 monthly 12514.46 daily 12522.94
More frequent compounding gives a little more money, but the increase gets smaller each time.