Compound Interest Calculator
Calculate compound interest with monthly contributions, solve for principal, rate, or time, and see a year-by-year growth breakdown.
PRESETS
Keyboard: Enter to calculate · Esc to reset
What Is the Compound Interest Calculator?
This calculator covers four compound interest scenarios in one tool: find the final amount, find the required starting principal, find the required interest rate, or find how long it takes to reach a goal. A year-by-year breakdown table and a stacked area growth chart show exactly how your money grows.
- ›Four solve modes, find final amount (A), required principal (P), required rate (r%), or required time (t). Switch between modes with one click.
- ›Monthly contributions, add regular deposits to model real savings plans. The per-period amount is automatically converted to match the chosen compounding frequency.
- ›Seven compounding frequencies, annual, semi-annual, quarterly, monthly, weekly, daily, and continuous. See exactly how frequency affects your returns.
- ›Effective Annual Rate (EAR), displayed for every calculation so you can compare products with different compounding schedules on equal footing.
- ›Year-by-year table, shows contributions added and interest earned for each year, up to 50 years of detail.
- ›Seven currencies, USD, EUR, GBP, CAD, AUD, INR, JPY with correct symbols throughout.
Formula
Compound Interest, Discrete Compounding
A = P (1 + r/n)^(n·t)
With Regular Contributions (PMT per period)
A = P(1 + r/n)^(n·t) + PMT × [(1 + r/n)^(n·t) − 1] / (r/n)
Continuous Compounding
A = P · e^(r·t)
Solve for Any Variable
Principal: P = A / (1 + r/n)^(n·t)
Rate: r = n × ((A/P)^(1/(n·t)) − 1)
Time: t = ln(A/P) / (n · ln(1 + r/n))
Effective Annual Rate (EAR)
EAR = (1 + r/n)^n − 1 [Continuous: EAR = e^r − 1]
| Symbol | Name | Description |
|---|---|---|
| A | Final amount | Total value of the investment at the end of the term |
| P | Principal | The initial investment or present value of the deposit |
| r | Annual interest rate | Expressed as a decimal: 5% → r = 0.05 |
| n | Compounding periods | Number of times interest is applied per year (monthly = 12) |
| t | Time | Investment duration in years; decimals allowed (e.g. 2.5) |
| PMT | Periodic contribution | Regular addition made at each compounding period |
| EAR | Effective annual rate | The true annual yield after accounting for compounding |
| e | Euler's number | Mathematical constant ≈ 2.71828; base of continuous compounding |
Compounding Frequency Comparison (5%, $10,000, 10 years)
Annually (n=1): A = $16,288.95 EAR = 5.0000%
Quarterly (n=4): A = $16,436.19 EAR = 5.0945%
Monthly (n=12): A = $16,470.09 EAR = 5.1162%
Daily (n=365): A = $16,486.65 EAR = 5.1267%
Continuous: A = $16,487.21 EAR = 5.1271%
How to Use
- 1Select a mode: Choose what you want to calculate: final amount (A), required principal (P), required rate (r%), or time needed (t).
- 2Choose currency and compounding: Pick your currency and how often interest compounds, from annually to continuously.
- 3Load a preset (optional): In Find Amount mode, choose from five real scenarios: savings account, retirement fund, education savings, term deposit, or long-term growth.
- 4Enter your values: Fill in the inputs shown for your chosen mode. Leave monthly contribution blank or 0 for lump-sum calculations.
- 5Calculate: Press Enter or click Calculate. The result appears prominently with six stat cards, a ratio bar, a growth chart, step-by-step working, and a year-by-year table.
- 6Review the breakdown: The growth chart shows principal (gray) vs interest earned (orange). The table shows exactly how much interest accrues each year.
- 7Compare scenarios: Change the compounding frequency or rate and recalculate instantly to compare outcomes. All inputs are saved to your browser so you never lose your work.
Example Calculation
Example 1: Savings account with monthly contributions
P = $10,000 | r = 4.5% | t = 5 years | n = 12 (monthly) | PMT = $200/month
Growth factor = (1 + 0.045/12)^(12×5) = (1.00375)^60 = 1.25161
Lump sum: $10,000 × 1.25161 = $12,516.07
Contributions: $200 × (1.25161 − 1) / 0.00375 = $13,408.47
Final Amount = $25,924.54
Total contributed: $22,000 | Interest earned: $3,924.54
Example 2: Find required rate to double $50,000 in 10 years
A = $100,000 | P = $50,000 | t = 10 years | n = 12 (monthly)
r = 12 × ((100,000/50,000)^(1/120) − 1)
r = 12 × ((2)^(1/120) − 1)
r = 12 × (1.005793 − 1) = 12 × 0.005793
Required Rate = 6.9517% per year
EAR = (1 + 0.069517/12)^12 − 1 = 7.19%
Example 3: Rule of 72 vs exact doubling time
| Rate | Rule of 72 | Exact (monthly) | Exact (daily) | Continuous |
|---|---|---|---|---|
| 3% | 24.0 yrs | 23.1 yrs | 23.1 yrs | 23.1 yrs |
| 5% | 14.4 yrs | 13.9 yrs | 13.9 yrs | 13.9 yrs |
| 7% | 10.3 yrs | 9.93 yrs | 9.90 yrs | 9.90 yrs |
| 10% | 7.20 yrs | 6.96 yrs | 6.93 yrs | 6.93 yrs |
| 12% | 6.00 yrs | 5.81 yrs | 5.78 yrs | 5.78 yrs |
Understanding Compound Interest
How Compound Interest Works
Compound interest earns interest on both the original principal and on all previously earned interest. Each compounding period, the interest earned is added to the balance, which then becomes the new base for the next calculation. This creates a self-reinforcing cycle that accelerates growth over time, the longer money compounds, the faster the snowball grows.
The contrast with simple interest is dramatic. At 7% simple interest, $10,000 earns a fixed $700 per year regardless of how long it has been invested. At 7% compound interest (annual), year 1 earns $700, year 10 earns $1,374, and year 20 earns $2,698, nearly four times as much as in year 1, all from the same original deposit.
Why compounding frequency matters less than you think
The jump from annual to monthly compounding on a 5% rate only increases the effective yield from 5.000% to 5.116%, a difference of $37 per year on $30,000. But the jump from monthly to continuous compounding adds barely $0.50 per year on the same balance. The math shows sharply diminishing returns as frequency increases, which is why the difference between "daily" and "continuous" compounding is almost negligible in practice.
The Rule of 72
The Rule of 72 is a quick mental shortcut: divide 72 by the annual interest rate percentage to estimate how many years it takes to double your money. At 6%, money doubles in roughly 72/6 = 12 years. At 9%, it doubles in about 8 years.
- ›The rule is most accurate for rates between 6% and 10%.
- ›For higher rates (>15%) or lower rates (<3%), the exact formula gives a more precise answer.
- ›The Rule of 72 also works in reverse: to double in 8 years, you need roughly 72/8 = 9% per year.
- ›A related rule: the Rule of 114 estimates tripling time, and Rule of 144 estimates quadrupling time.
Effective Annual Rate (EAR), The True Yield
Financial products advertise a nominal rate (also called APR in some contexts), but the Effective Annual Rate (EAR) tells you what you actually earn after compounding. Two accounts with the same nominal rate can have different true yields depending on how often they compound.
EAR = (1 + r/n)^n − 1
Example: 6% nominal, monthly compounding
EAR = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 = 6.168%
The true return is 6.168%, not 6%, compare products using EAR, not nominal rate.
Regular Contributions, The Power of Dollar-Cost Averaging
Adding regular deposits transforms compound interest from a single-investment concept into a wealth-building strategy. The future value of an annuity formula shows that consistent monthly contributions often matter more than the initial lump sum for long investment horizons:
- ›$10,000 lump sum at 7% for 30 years → $76,123 (no contributions)
- ›$0 lump sum + $200/month at 7% for 30 years → $226,072 (contributions only)
- ›$10,000 lump sum + $200/month at 7% for 30 years → $302,195 (combined)
The monthly contributions produce nearly 3× the lump sum alone because each deposit has time to compound. This is why starting early matters far more than starting with a large amount.
Real-world example: retirement savings
Two investors both retire at 65 with the same rate (7%, monthly compounding). Investor A starts at 25 and contributes $300/month for 40 years. Investor B starts at 35 and contributes $600/month for 30 years (twice as much, half the time). Investor A ends with $792,000; Investor B ends with $679,000. Starting a decade earlier beats doubling the contribution, the lost decade of compounding is worth more than the extra $300/month.
Continuous Compounding
Continuous compounding is the mathematical limit as compounding frequency approaches infinity. Rather than applying interest n times per year, it applies infinitesimally often, resulting in A = Pe^(rt). In practice, no financial product truly compounds continuously, but the formula is used extensively in mathematical finance, options pricing (Black-Scholes), and bond valuation.
The difference between daily compounding and continuous compounding is negligible for personal finance, but understanding the formula is important for anyone studying finance theory or working with derivative pricing.
When Compound Interest Works Against You
The same exponential growth that builds wealth in savings accounts destroys it in debt. Credit card balances at 20–25% APR compound monthly, meaning a $5,000 balance grows to $8,954 in 5 years without payments, and to $48,252 in 20 years. The mathematics are identical to savings; only the direction differs.
- ›Pay off high-interest debt before investing: a 20% credit card is a guaranteed 20% return when paid down.
- ›Minimum payments on revolving credit are designed to keep balances compounding as long as possible.
- ›Student loans, auto loans, and mortgages all use compounding, the amortization schedule front-loads interest.
- ›Compare loan APRs using EAR, not the nominal rate, to find the true cost of borrowing.
Frequently Asked Questions
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal every period. Compound interest is calculated on the principal plus all accumulated interest from previous periods.
- ›Simple: $10,000 at 5% for 10 years → $15,000 ($5,000 total interest, flat each year).
- ›Compound (annual): $10,000 at 5% for 10 years → $16,288.95 ($6,288.95 total interest, growing each year).
- ›The difference is $1,288.95, from interest earning interest.
- ›Over 30 years, the gap explodes: simple gives $25,000; compound (annual) gives $43,219.
For savings and investments, you want compound interest. For loans, simple interest costs less.
How does compounding frequency affect my returns?
More frequent compounding means interest starts earning interest sooner, producing slightly higher returns. However, the benefit diminishes sharply as frequency increases:
- ›Annual → Monthly: adds ~0.12% to effective yield at 5% nominal rate.
- ›Monthly → Daily: adds only ~0.011% more.
- ›Daily → Continuous: adds barely 0.001% more.
The big practical takeaway: the difference between "monthly" and "daily" compounding is nearly invisible. What matters far more is the nominal rate itself and how long the money is invested.
What is the Effective Annual Rate (EAR) and why does it matter?
The EAR (also called the Annual Equivalent Rate or AER) is the true annual return after accounting for compounding within the year.
- ›Formula: EAR = (1 + r/n)^n − 1
- ›A 6% nominal rate compounded monthly → EAR = 6.168%.
- ›A 6% nominal rate compounded quarterly → EAR = 6.136%.
- ›A 6% nominal rate compounded annually → EAR = 6.000% (same as nominal).
Always compare savings accounts, CDs, and bonds using EAR, not the advertised nominal rate. Two products with the same nominal rate can have meaningfully different effective yields.
What is the Rule of 72?
The Rule of 72 is a mental math shortcut for estimating how long it takes to double your money at a given interest rate:
- ›Doubling time ≈ 72 / annual rate (%)
- ›At 6%: doubles in ~12 years
- ›At 9%: doubles in ~8 years
- ›At 12%: doubles in ~6 years
It also works in reverse: to double in 10 years, you need about 72/10 = 7.2% per year.
The rule is most accurate between 6–10%. For very high or very low rates, use the exact formula: t = ln(2) / (n × ln(1 + r/n)).
How do regular monthly contributions change the calculation?
Regular deposits use the future value of an annuity formula added to the lump-sum formula:
- ›A = P(1+r/n)^(n·t) + PMT × [(1+r/n)^(n·t) − 1] / (r/n)
- ›PMT is the contribution per compounding period (this calculator converts your monthly input automatically).
- ›Each deposit starts compounding from the moment it is made.
- ›Contributions made earlier benefit from more compounding time, hence the huge impact of starting early.
Example: at 7%, $200/month for 30 years produces $226,000 from $72,000 contributed. The other $154,000 is pure compound interest, more than double what you put in.
What is continuous compounding and how is it different from daily?
Continuous compounding is the theoretical limit as compounding frequency approaches infinity. The formula simplifies to A = Pe^(rt).
- ›Daily compounding (n=365) at 5% on $10,000 for 10 years: $16,486.65
- ›Continuous at 5% on $10,000 for 10 years: $16,487.21, just $0.56 more.
- ›The practical difference is negligible for personal finance.
- ›Continuous compounding is important in mathematical finance, options pricing, and bond theory.
No real bank account uses continuous compounding. If you see it advertised, it is theoretical.
Can I use this calculator for debt and loans?
Yes, the math is identical whether the balance is growing in your favour (savings) or against you (debt). Enter your loan balance as the principal and your interest rate as the rate.
- ›Credit cards typically compound daily or monthly, use n=365 or n=12.
- ›To see how fast a balance grows with no payments, set contributions to 0.
- ›To estimate payoff time, use the "Find Time" mode with your current balance as P and 0 as A minus target payoff.
- ›For full loan amortization with monthly payments, use the Loan Payment Calculator instead.
Understanding the compounding math helps explain why minimum-payment-only strategies can keep balances growing for decades.
Does the calculator save my inputs automatically?
Yes, all inputs are automatically saved to your browser's localStorage after every calculation:
- ›The selected mode, principal, target amount, rate, time, compounding frequency, monthly contribution, and currency are all saved.
- ›Everything is stored locally in your browser, nothing is sent to any server.
- ›Your inputs are restored automatically the next time you visit the page.
- ›Click Reset or press Esc to clear all fields and remove the saved data.
The calculator also works offline once the page has loaded.