What is Compound Interest?
How compound interest works, the formula, and why starting early makes such a dramatic difference.
Compound interest vs. simple interest
Simple interest is calculated only on the original amount you deposited — the principal. Every period, you earn the same fixed amount and nothing more.
Compound interest is different: each period, you earn interest on your principal plus all the interest you have already accumulated. Your interest earns interest. That feedback loop is what makes compounding so powerful over time.
Quick comparison — $10,000 at 7% for 10 years:
- Simple interest: $10,000 + ($700 × 10) = $17,000
- Compound interest (annual): $19,671.51
The $2,671 difference is entirely from interest earning interest.
Albert Einstein supposedly called compound interest the eighth wonder of the world — apocryphal or not, the math backs it up.
The compound interest formula
The standard formula for compound interest is:
A = P(1 + r/n)^(nt)
Where each variable means:
A— the final amount (principal + all accumulated interest)P— the principal, meaning the starting balance or initial depositr— the annual interest rate expressed as a decimal (e.g. 7% → 0.07)n— the number of times interest compounds per year (12 for monthly, 365 for daily, 1 for annually)t— the time in years
The key insight is the exponent nt. As time increases, you are raising a number greater than 1 to a larger and larger power — which is why the growth curve bends upward dramatically over long periods.
Worked example: $10,000 over 30 years
Suppose you invest $10,000 at an annual rate of 7%, compounded monthly, for 30 years.
P = 10,000 r = 0.07 n = 12 (monthly) t = 30 A = 10,000 × (1 + 0.07/12)^(12×30) A = 10,000 × (1.005833...)^360 A = 10,000 × 8.1165... A ≈ $81,165
Your $10,000 grows to roughly $81,165 — more than eight times your original deposit. You contributed $10,000 and the remaining $71,165 is pure compounded interest.
For context: at simple interest, the same $10,000 at 7% for 30 years would be just $10,000 + ($700 × 30) = $31,000. Compounding adds another $50,000 on top.
Why starting early matters so much
The most underappreciated fact about compounding is how sensitive it is to time. Because growth is exponential, adding years at the beginning of the period is far more valuable than adding years at the end.
The Rule of 72
A quick mental shortcut: divide 72 by your annual interest rate to find approximately how many years it takes your money to double.
At 6% → 72 / 6 = 12 years to double At 7% → 72 / 7 ≈ 10 years to double At 9% → 72 / 9 = 8 years to double At 12% → 72 / 12 = 6 years to double
So at 7%, money doubles roughly every 10 years. $10,000 invested at age 25 doubles to $20,000 by 35, $40,000 by 45, $80,000 by 55, and $160,000 by 65. The same $10,000 invested at age 35 reaches only $80,000 by 65 — half as much, simply because it missed one doubling period.
This is why financial planners emphasize starting early above almost everything else. Contribution size matters, but time in the market is the most powerful lever available to individual investors.
Does compounding frequency matter?
More frequent compounding produces slightly higher returns, but the differences are smaller than most people expect. Here is $10,000 at 7% for 30 years across different frequencies:
Annual (n=1): $76,122.55 Monthly (n=12): $81,164.88 Daily (n=365): $81,637.38 Continuous: $81,674.93
The jump from annual to monthly compounding adds about $5,000 over 30 years — meaningful, but not transformative. Going from monthly to daily adds only another $472. At typical savings account or investment rates, the difference between monthly and daily compounding is negligible in practice.
What matters far more than compounding frequency: the interest rate itself, the amount you invest, and how long you leave it untouched.
Frequently asked questions
- Is compound interest good or bad?
- Both, depending on which side of it you are on. As a saver or investor, compound interest works in your favor — your money grows exponentially over time. As a borrower, especially on credit card debt or payday loans, compound interest works against you for exactly the same reason. High-interest debt compounds just as relentlessly as a well-performing investment. Paying off compound-interest debt is almost always the highest guaranteed return available to you.
- What is the best compounding frequency?
- More frequent compounding is marginally better for savers, but the difference between daily and monthly compounding is tiny at typical interest rates. The advertised compounding frequency is less important than the actual APY (Annual Percentage Yield), which already factors in how often interest is compounded. When comparing savings accounts or investments, compare APYs directly rather than trying to compare stated rates with different compounding frequencies.
- How does compound interest differ from APR?
- APR (Annual Percentage Rate) is the simple annual rate without factoring in compounding. APY (Annual Percentage Yield) is the effective annual rate after compounding is applied. For example, a 12% APR compounded monthly produces a 12.68% APY — the extra 0.68% comes from compounding. When evaluating savings accounts, look at the APY. When evaluating loans, lenders are required to disclose the APR, but be aware that interest often compounds monthly, making the true cost higher than the APR suggests.