Quick Answer
Compound interest is calculated using A = P(1 + r/n)^(nt), where P is the initial principal, r is the annual interest rate, n is the number of times interest compounds per year, and t is the number of years.
What Is Compound Interest?
Compound interest is interest calculated not just on your original principal, but also on all the interest that has accumulated in previous periods. This is fundamentally different from simple interest, where interest is only ever calculated on the original amount.
The effect of compounding is often described as 'interest earning interest', and over long time horizons, this effect becomes dramatic. Albert Einstein is widely (though apocryphally) quoted as calling compound interest 'the eighth wonder of the world,' and while the quote's origin is disputed, the underlying math is very real: money compounding at even modest rates can grow substantially over 10, 20, or 30 years.
Compound interest works both for you and against you. It's the mechanism behind growing savings accounts, mutual funds, and retirement investments, but it's also the mechanism behind credit card debt growing faster than expected if only minimum payments are made.
In Practice
Two colleagues both receive a $5,000 bonus. The first puts it in a savings account at 2% simple interest. After 20 years he has $7,000. The second invests the same amount in an index fund averaging 8% compound annual growth. After 20 years she has $23,305 — more than three times as much on the same starting amount. The difference is not discipline or luck. It is entirely the mathematics of compounding: her returns in year 10 earned returns in years 11 through 20. The first colleague's money never worked for itself.
How to Use
- 1Enter your initial principal (the starting amount you're investing or saving).
- 2Enter the annual interest rate offered.
- 3Select how often interest compounds, daily, monthly, quarterly, or annually.
- 4Enter the number of years you plan to leave the money invested.
- 5The calculator shows your final balance and the total interest earned.
Formula
A = P × (1 + r/n)^(n×t)A = final amount, P = principal, r = annual rate (decimal), n = compounding periods per year, t = years
Interest = A − PExample: PKR 100,000 invested at 10% annual interest, compounded monthly, for 5 years
- P = 100,000, r = 0.10, n = 12, t = 5
- A = 100,000 × (1 + 0.10/12)^(12×5)
- A = 100,000 × (1.00833)^60
- A ≈ 164,530
Common Mistakes to Avoid
✕ Entering the annual rate when your account pays monthly or quarterly
✓ If your savings account states a monthly rate of 0.5%, the annual rate is approximately 6%. Always confirm whether your bank's quoted rate is annual, monthly, or per period — then convert before entering into this calculator.
✕ Confusing compound interest with simple interest totals
✓ Simple interest grows linearly. Compound interest grows exponentially. For short periods (1-2 years) the difference is small. Over 10-30 years it becomes enormous. Make sure your calculator is set to the compounding frequency your investment actually uses.
Tips & Things to Know
- More frequent compounding (daily or monthly vs. annually) results in slightly higher returns at the same stated annual rate, always check the compounding frequency when comparing investment products.
- Time is the single biggest lever in compound growth, starting to invest even a few years earlier often outweighs the benefit of a higher interest rate over the same horizon.
- Compound interest applies to debt too, credit cards typically compound daily, which is why balances can grow quickly if only minimum payments are made.
- The 'Rule of 72' is a quick mental shortcut: divide 72 by the annual interest rate to estimate how many years it takes for an investment to double.