Quick idea
Compound interest means you earn returns on your original money and on the returns you’ve already earned. Over time, that “returns-on-returns” effect can become the biggest part of your growth.
Table of contents
Simple vs compound interest
Simple interest only earns on the original principal. If you put in $10,000 at 5% simple interest, you earn $500 per year, every year (as long as the principal stays the same).
Compound interest earns on the growing balance. In early years, the growth looks similar to simple interest. In later years, the interest itself becomes a bigger number because the balance is bigger.
The compound interest formula
The standard formula (no ongoing contributions) is:
A = P (1 + r/n)^(n·t)
- A = ending amount
- P = starting principal (your initial balance)
- r = annual interest rate (as a decimal, so 7% = 0.07)
- n = number of compounding periods per year (12 monthly, 365 daily, etc.)
- t = time in years
Compounding frequency (APY vs APR)
If you compound more frequently (monthly vs yearly), you earn a tiny bit more because interest is credited sooner. The difference is usually small at normal rates, but it’s real.
Effective APY formula:
APY = (1 + r/n)^n − 1
Adding contributions over time
Contributions often matter more than the rate in the first few years. If you add money monthly, your account grows from both:
- New contributions you add
- Returns earned on the whole balance (including prior contributions)
Contribution timing (beginning vs end)
If you contribute at the beginning of the period, that money has more time to grow. Beginning-of-period contributions will always end higher than end-of-period contributions (all else equal).
- End of period: contribution after interest is applied (common assumption)
- Beginning of period: contribution before interest is applied (slightly higher ending value)
Inflation: “today’s dollars”
A balance of $200,000 in 20 years will not buy what $200,000 buys today. Inflation-adjusting (a “real” view) helps you understand future purchasing power.
(1 + i)^t,
where i is inflation and t is years.
Inflation is unpredictable; using a steady average rate is just a planning tool.
Taxes and “tax drag”
In taxable accounts, investment gains can be taxed (interest, dividends, and realized capital gains). Taxes reduce how much money stays invested, which reduces compounding—this is sometimes called tax drag.
Tax rules vary by country, state, and account type. This is educational only.
Examples you can copy
These are simplified examples to build intuition.
| Scenario | Start | Rate | Years | Contribution | Big takeaway |
|---|---|---|---|---|---|
| One-time deposit | $10,000 | 7% | 20 | None | Time does the heavy lifting |
| Monthly contributions | $1,000 | 7% | 20 | $200/mo | Contributions dominate early |
| Higher rate, same time | $10,000 | 9% | 20 | None | Rate matters, but time still wins |
| Same rate, more time | $10,000 | 7% | 30 | None | Extra decade is huge |
72/8 ≈ 9 years to double (rough estimate).
Common mistakes
- Mixing APR and APY: for savings, APY is usually what you actually earn.
- Ignoring fees: even small annual fees reduce compounding long-term.
- Forgetting inflation: nominal balances can look big but buy less.
- Assuming a fixed rate: markets vary; use ranges and scenarios.
- Counting taxes wrong: taxable vs tax-advantaged accounts compound differently.
FAQ
Is compounding always a good thing?
Compounding helps investments grow, but it also works against you with debt (credit cards, high APR loans). If you’re paying high APR, paying debt down can be a “guaranteed return” compared to investing.
What rate should I use?
Use something realistic for the account type (savings vs bonds vs diversified stocks). For planning, try multiple rates (e.g., 5%, 7%, 9%) and treat them as scenarios—not promises.
What’s the difference between nominal and real returns?
Nominal return is the quoted rate. Real return subtracts inflation (roughly). Real return is what matters for purchasing power.
Does contribution timing really matter?
It can—especially over long time frames. Beginning-of-period contributions earn interest for more time, so they end higher. The difference is usually modest but consistent.
What about deposits made throughout the month?
Then your result is between “beginning” and “end” assumptions. A schedule-based calculator is best for modeling this realistically.