The Power of Compound Interest
Albert Einstein reportedly called compound interest the "eighth wonder of the world." This calculator shows you exactly how much your money grows over time - with or without regular contributions. See the difference between simple and compound interest, and understand why starting early matters more than investing more.
What Is Compound Interest?
Compound interest means your interest earns interest. Instead of earning a return only on your original deposit, you earn it on your growing balance.
Over decades, this compounds dramatically. $10,000 at 7% for 30 years grows to $76,123 without adding a dollar.
The Compound Interest Formula
- A = final amount
- P = principal (initial amount)
- r = annual interest rate (decimal)
- n = compounding frequency per year
- t = time in years
Compounding Frequency Comparison
$10,000 at 6% for 10 years:
| Frequency | Final Amount | Total Interest |
|---|---|---|
| Annually | $17,908 | $7,908 |
| Semi-annually | $18,061 | $8,061 |
| Quarterly | $18,140 | $8,140 |
| Monthly | $18,194 | $8,194 |
| Daily | $18,221 | $8,221 |
| Continuous | $18,221 | $8,221 |
Why Starting Early Matters
Two investors, both earn 7% annual returns:
| Investor | Monthly Contribution | Years Investing | Total Contributed | Final Balance |
|---|---|---|---|---|
| Sarah (starts at 25) | $200 | 40 years | $96,000 | $525,000 |
| Mike (starts at 35) | $300 | 30 years | $108,000 | $365,000 |
Sarah contributes less but ends with $160,000 more. Time beats amount.
The Rule of 72
To estimate how many years it takes to double your money, divide 72 by your interest rate:
- 5% return: 72/5 = 14.4 years to double
- 7% return: 72/7 = 10.3 years
- 10% return: 72/10 = 7.2 years
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest pays only on the principal. Compound interest pays on the principal plus accumulated interest. Compound always wins over time.
How does compounding frequency affect returns?
More frequent compounding means slightly more interest. Daily vs annual compounding adds about 0.2% per year on a 6% account.
What is continuous compounding?
The mathematical limit where interest compounds infinitely often. Formula: A = P × e^(rt). Rare in practice but common in finance theory.
How do I use compound interest for retirement?
Invest early, contribute consistently, choose low-fee index funds. At 7% average return, money doubles every ~10 years.
What is the Rule of 72?
Divide 72 by your interest rate to estimate doubling time. Simple mental math for planning.
Does compound interest work against me?
Yes - credit card debt compounds monthly. A 24% APR balance grows faster than most investments.