Compound interest is the reason a modest deposit can grow into a serious sum over time — and the reason debt can spiral if you ignore it. The magic is that you earn interest on your interest, not just on your original money. Let's break down the formula and prove it with numbers.
Simple interest vs. compound interest
Simple interest is calculated only on the original principal:
- I = P × r × t
where P is the principal, r is the annual rate (as a decimal), and t is the number of years.
Example: $1,000 at 5% simple interest for 3 years.
- I = 1,000 × 0.05 × 3 = $150
- Final balance = $1,150
Compound interest adds each period's interest back into the balance, so the next period earns even more.
The compound interest formula
A = P × (1 + r/n)^(n × t)
- A = final amount
- P = principal (starting balance)
- r = annual interest rate (decimal)
- n = number of times interest compounds per year
- t = number of years
Example: $1,000 at 5%, compounded annually (n = 1) for 3 years.
- A = 1,000 × (1 + 0.05/1)^(1×3)
- A = 1,000 × (1.05)^3
- A = 1,000 × 1.157625 = $1,157.63
That's $7.63 more than simple interest earned over the same period — and the gap widens dramatically over longer horizons.
Why compounding frequency matters
The more often interest compounds, the faster your money grows. Using the same $1,000 at 5% for 3 years:
- Annually (n = 1): $1,157.63
- Monthly (n = 12): 1,000 × (1 + 0.05/12)^(36) ≈ $1,161.47
- Daily (n = 365): ≈ $1,161.83
The jumps get smaller as frequency increases, but more frequent compounding always wins. This is why savings accounts advertise an APY (which bakes in compounding) rather than just a flat rate.
How to use it
You don't need to crunch exponents by hand. Open the Interest Calculator, enter your principal, rate, term, and compounding frequency, and it shows your final balance plus the total interest earned.
A few practical takeaways:
- Start early. Time is the most powerful variable in the formula because the exponent grows with t.
- Watch the rate. Even a 1% difference compounds into a large gap over decades.
To explore how those percentages stack up, try the Percentage Calculator. And if you're on the borrowing side of the equation, the Loan Calculator shows how compounding works against you when you pay interest instead of earning it.