Key takeaways
- Compound interest is A = P(1 + r/n)^(n×t), with r as a decimal.
- n is the compounding frequency: 12 for monthly, 4 for quarterly, 1 for yearly.
- A is the total balance, so subtract P to get just the interest earned.
- More frequent compounding (higher n) grows a balance faster at the same rate.
- It always beats simple interest over time, because interest starts earning interest.
In this guide
What is compound interest?
With simple interest, you always earn interest on the same starting amount. With compound interest, the interest earned gets added back to the balance, so the next round of interest is calculated on a slightly bigger number. This repeats every compounding period, which is why savings and debt can both grow faster than people expect.
Why does compound interest matter?
Compound interest is why long-term savings can grow so much faster than short-term ones, and why credit card debt can spiral if left unpaid. The gap between simple and compound interest widens every year the money stays invested or owed.
$5,000 at 6% for 5 years earns $1,500 with simple interest, but $1,744.25 with interest compounded monthly — about 16% more, from the exact same rate.
The formula
| Symbol | What it means | Example |
|---|---|---|
| A | Final amount after t years, including principal | $6,744.25 |
| P | Principal — the amount you start with | $5,000 |
| r | Annual interest rate as a decimal | 0.06 (for 6%) |
| n | Compounding periods per year | 12 (monthly) |
| t | Total time, in years | 5 |
How to calculate compound interest step by step
- 1Divide r by n. This gives the interest rate for a single compounding period.
- 2Add 1. You now have the growth factor for one period.
- 3Multiply n by t. This gives the total number of compounding periods over the whole term.
- 4Raise the growth factor to that power. This is
(1 + r/n)^(n×t). - 5Multiply by P. The result is A, the final balance. Subtract P if you only want the interest.
See how changing the compounding frequency changes the outcome using the calculator below.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Using the wrong n. Monthly compounding means n = 12, not n = 1. A smaller n understates how fast the balance grows.
- Entering the rate as a whole number. 6% must be typed as 0.06, exactly like with the simple interest calculator.
- Forgetting the exponent applies to the whole bracket.
(1 + r/n)is calculated first, then raised to the power ofn × t— not the other way around.
Tips and tricks
- Yearly compounding (n = 1) simplifies to
A = P(1 + r)ᵗ, the same formula the future value calculator uses. - To compare investments fairly, keep n and t consistent — a 6% rate compounded monthly is not the same as 6% compounded yearly.
- Working backwards from a target amount to the rate you'd need? Try the CAGR calculator, which solves for the steady annual growth rate between two values.
Where you'll use it in real life
- Savings accounts and fixed deposits: most banks compound interest monthly or quarterly, not just once a year.
- Credit cards and loans: unpaid balances often compound too, which is why debt can grow quickly if minimum payments barely cover the interest.
- Retirement planning: even small monthly contributions can grow substantially over decades thanks to compounding.
- Comparing investments: the EMI calculator uses the same compounding idea, but for loan repayments instead of savings growth.
Quick summary
Compound interest grows a balance using A = P(1 + r/n)^(n×t): divide the rate by the compounding frequency, raise it to the power of the total periods, then multiply by the principal. The more often interest compounds, the faster the balance grows. Try the calculator above with your own numbers to see the effect.
Worked example
You deposit $5,000 into a savings account with a 6% annual interest rate, compounded monthly, and leave it untouched for 5 years.
- 01A = P(1 + r/n)^(nt)
- 02A = 5000(1 + 0.06/12)^(12×5)
- 03A = 5000(1.005)^60
- 04A = $6,744.25
These numbers are pre-filled in the calculator above.
Frequently asked questions
How is compound interest different from simple interest?
Simple interest is always calculated on the original principal. Compound interest adds earned interest back to the balance, so it earns interest too — which is why compound growth speeds up over time.
What does compounding monthly versus yearly change?
More frequent compounding means interest is added to the balance more often, so each new calculation starts from a slightly larger number. Monthly compounding (n = 12) grows a balance faster than yearly compounding (n = 1) at the same rate.
How do I find just the interest earned, not the total balance?
Calculate A using the formula, then subtract the original principal P. The result, A − P, is the interest earned.
Why is the rate entered as a decimal?
The formula multiplies and raises powers using the rate directly, so a percentage has to be converted first. Divide the percentage by 100 — 6% becomes 0.06.
