Compound Interest Calculator — With Formula Shown
Free Compound Interest Calculator — See Your Money Grow
Calculate how any investment or savings grows with compound interest. Add monthly contributions, choose your compounding frequency, and see your final balance year by year. The formula is shown with every result. No sign-up, no ads, completely free.
📈 Enter Your Investment Details
How to Use This Compound Interest Calculator
- Initial Investment — the amount you start with. Can be $0 if you’re starting from scratch with only monthly contributions.
- Monthly Contribution — how much you add every month. Enter 0 if you’re making a single lump-sum investment only.
- Annual Interest Rate — the annual return rate. For stock market estimates, a common long-term figure is 7–10%. For high-yield savings, 4–5%. For CDs, 4–5.5%.
- Time Period — how many years you plan to invest or save.
- Compounding Frequency — how often interest is calculated and added. Monthly is the most common for savings accounts and investments.
- Inflation Rate (optional) — if entered, the calculator also shows your balance in today’s purchasing power (real value).
What Is Compound Interest? — Simply Explained
Compound interest means earning interest on your interest. When your savings earn interest, that interest is added to your balance. In the next period, you earn interest on the larger amount — including the interest already earned. This cycle repeats every compounding period, causing your money to grow exponentially over time.
💡 Simple vs. Compound Interest — The Key Difference
Simple interest: $10,000 at 7% for 20 years = $10,000 + (10,000 × 7% × 20) = $24,000
Compound interest (annual): $10,000 at 7% for 20 years = 10,000 × (1.07)²0; = $38,697
Compound interest (monthly): $10,000 at 7% for 20 years = $40,064
Compounding monthly vs. simple interest earns you $16,064 more on the same deposit.
The compound interest formula
A = P(1 + r/n)^(nt)
- A = Final amount
- P = Principal (initial investment)
- r = Annual interest rate as a decimal (e.g., 7% = 0.07)
- n = Compounding frequency per year (12 for monthly)
- t = Time in years
When you add regular contributions (PMT per month), the formula expands to: A = P(1+r/n)^(nt) + PMT × [((1+r/n)^(nt) − 1) ÷ (r/n)]
Why compounding frequency matters
| Frequency | $10,000 at 7% for 20 years | Difference vs. annual |
|---|---|---|
| Annually | $38,697 | — |
| Quarterly | $39,751 | +$1,054 |
| Monthly | $40,064 | +$1,367 |
| Daily | $40,138 | +$1,441 |
The Rule of 72 — Quick Mental Math for Doubling Time
The Rule of 72 is a simple shortcut to estimate how long it takes for an investment to double: divide 72 by the annual interest rate.
| Annual Rate | Approximate Doubling Time | Example |
|---|---|---|
| 3% | 24 years | Inflation-matching savings |
| 5% | 14.4 years | High-yield savings / CDs |
| 7% | 10.3 years | S&P 500 historical avg (inflation-adjusted) |
| 10% | 7.2 years | S&P 500 nominal historical avg |
| 12% | 6 years | Aggressive growth estimates |
Example: At 7% annual return, your money doubles every ~10 years. Start with $10,000 at age 25 and by age 65 it becomes approximately $160,000 — without adding a single dollar more.
Compound Interest Examples
Start: $5,000 | Monthly: $300
Rate: 7% | Time: 30 years
Final balance: ~$374,000
Deposited: $113,000 | Interest: $261,000
Start: $10,000 | Monthly: $200
Rate: 4.5% | Time: 10 years
Final balance: ~$46,000
Deposited: $34,000 | Interest: $12,000
Start: $50,000 | Monthly: $0
Rate: 8% | Time: 25 years
Final balance: ~$342,000
Pure power of compounding over time
Start: $0 | Monthly: $100
Rate: 7% | Time: 40 years
Final balance: ~$262,000
Deposited only $48,000 over 40 years
Frequently Asked Questions
What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus all previously earned interest. Over long periods, compound interest grows exponentially while simple interest grows linearly, making the difference enormous over decades.
What interest rate should I use for retirement calculations?
Financial planners commonly use 6–7% for long-term retirement projections with a diversified portfolio. This reflects the S&P 500’s historical average of ~10% minus average inflation of ~3%. For more conservative projections, use 5%. These are estimates — actual returns vary by year and portfolio.
How does monthly contribution affect final balance?
Dramatically. Adding $200/month to a $5,000 investment at 7% for 30 years grows to ~$374,000. Without contributions, the same $5,000 grows to only ~$38,000. Regular contributions often matter more than the starting amount, especially over long timeframes.
Is more frequent compounding always better?
Yes, but the difference between monthly and daily compounding is very small (usually less than 0.1%). The difference between annual and monthly compounding is more meaningful over long periods. For practical purposes, monthly compounding (used by most banks and investment accounts) is essentially optimal.
What is the Rule of 72?
A mental math shortcut: divide 72 by the annual interest rate to estimate how many years it takes for money to double. At 6%, money doubles in 72/6 = 12 years. At 9%, it doubles in 8 years. It’s an approximation — accurate within 1–2 years for rates between 4% and 12%.
What does the inflation adjustment show?
When you enter an inflation rate, the calculator shows your future balance in today’s purchasing power (real value). For example, if your balance grows to $500,000 in 30 years but inflation averaged 3%, that $500,000 has the purchasing power of about $206,000 in today’s dollars. This helps you plan for real wealth, not just nominal numbers.
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