The balance grows on itself
Compound interest pays you on the interest you have already earned, not just the original deposit, so the growth curve bends upward over time. The future value depends on the rate, how many times a year it compounds, and how long you leave it.
P is the starting amount, r the annual rate as a decimal, n the times it compounds each year, and t the years. Continuous compounding is the limit of that, A = Pert, and barely beats daily.
Why the rate matters more than it looks
Because growth is exponential, a small bump in the rate compounds into a large gap over decades. This is $10,000 left untouched for 30 years.
| Rate | After 30 years | Doubles every (Rule of 72) |
|---|---|---|
| 4% | $32,434 | 18 years |
| 6% | $57,435 | 12 years |
| 8% | $100,627 | 9 years |
| 10% | $174,494 | 7.2 years |
Six percentage points on the rate turns $32k into $174k — more than five times as much — from the same $10,000.
Contributions, timing and frequency
- Regular deposits add their own compounding. Each contribution earns interest for the time it is invested. $1,000 a year at 6% for 10 years grows to about $13,181 — well above the $10,000 paid in.
- Pay in at the start of the period. Contributing at the beginning of each period rather than the end gives every deposit one extra compounding step, worth roughly $791 over that same 10-year run.
- Effective rate beats the nominal one. A nominal 6% compounded monthly actually returns about 6.17% a year once the compounding is counted, using EAR = (1 + r/n)n − 1.
Common questions
What is the difference between simple and compound interest?
Simple interest is paid only on your original deposit. Compound interest is paid on the deposit plus all the interest already earned, so the balance grows on itself. Over $1,000 at 5% for 10 years, simple gives $1,500 while compounding gives about $1,629.
How often should interest compound?
More often is slightly better for you, but the effect is small. On $1,000 at 5% for a year, annual compounding earns $50.00 and daily earns $51.27. Over long horizons the rate and the years matter far more than the frequency.
How long will it take my money to double?
Divide 72 by the interest rate. At 6% that is 72 / 6 = 12 years; at 9% it is 8 years. The Rule of 72 is a close estimate for rates between about 6% and 10%.
