Compound Interest Calculator
Use the sliders or type the values.
$
%
years
$
Final balance:
Total deposited:
Interest earned:
Effective annual rate:
With simple interest:
Compound advantage:
A math tool, not financial advice: real rates change, and real accounts charge fees and taxes that are not included here.
Calculation:
This compound interest calculator shows how much money you will have at the end of a term when the interest you earn is added to the balance and starts earning interest of its own. Enter the starting amount, the annual rate, the years and how often interest compounds. If you like, add a monthly deposit.
The chart splits each year into what you put in and what interest earned, and a dashed line shows what you would have with simple interest. Below you will find the formula, worked examples, tables and common questions.
How to use the compound interest calculator
Step 1: Enter the starting amount, the annual interest rate (for example 5) and the years. You can type the values or move the sliders.
Step 2: Pick how often interest compounds: annually, semiannually, quarterly, monthly, daily or continuously.
Step 3: If you will add money every month, enter the monthly deposit. It is added at the end of each month. Leave it blank if there are no deposits.
Step 4: Click Calculate or press Enter. You get the final balance, the interest earned, the chart by year and the table. Results also update as you type.
Compound interest formula
With a starting amount P, an annual rate r (as a decimal), n compounding periods per year and t years, the final balance is:
| A = P × (1 + r ÷ n)n × t |
The interest earned is A - P. With continuous compounding you use the constant e (2.71828...):
| A = P × er × t |
Simple interest, by contrast, is always figured on the starting amount and never builds on itself:
| A = P × (1 + r × t) |
When there is a monthly deposit C at the end of each month, the calculator uses the equivalent monthly growth factor g = (1 + r ÷ n)n ÷ 12 and adds the deposits with the sum of a geometric series, where m = 12 × t is the number of months:
| A = P × gm + C × (gm - 1) ÷ (g - 1) |
The term is rounded to whole months. The effective annual rate, (1 + r ÷ n)n - 1, is how much money really grows in one year with that compounding.
Compound interest examples
Example 1: $10,000 at 5% a year for 10 years
Compounding is monthly (n = 12) and there are no deposits:
A = $10,000.00 × (1 + 0.05 ÷ 12)12 × 10 = $10,000.00 × 1.6470095 = $16,470.09
The interest earned is $16,470.09 - $10,000.00 = $6,470.09. With simple interest you would have $10,000.00 × (1 + 0.05 × 10) = $15,000.00, so compounding gives you $1,470.09 more.
Example 2: How often interest compounds
With the same amount, rate and term, compounding more often gives a little more money, but the gain levels off quickly:
| Compounding | Final balance | Interest earned |
|---|---|---|
| Annually | $16,288.95 | $6,288.95 |
| Semiannually | $16,386.16 | $6,386.16 |
| Quarterly | $16,436.19 | $6,436.19 |
| Monthly | $16,470.09 | $6,470.09 |
| Daily | $16,486.65 | $6,486.65 |
| Continuously | $16,487.21 | $6,487.21 |
Example 3: $1,000 to start and $200 a month at 7% for 20 years
With monthly compounding, g = (1 + 0.07 ÷ 12)12 ÷ 12 = 1.00583333 and m = 240 months:
Principal part: $1,000.00 × 1.00583333240 = $4,038.74
Deposits part: $200.00 × (1.00583333240 - 1) ÷ (1.00583333 - 1) = $104,185.33
The final balance is $4,038.74 + $104,185.33 = $108,224.07. You put in $49,000.00 ($1,000.00 plus 240 deposits of $200.00), and the rest, $59,224.07, is interest.
Example 4: How long does it take to double your money at 6% a year?
With annual compounding, 1.06t = 2, so t = ln 2 ÷ ln 1.06 = 11.9 years
The rule of 72 gives a quick estimate: 72 ÷ 6 = 12 years. It lands close to the exact value.
Table: years to double your money
Exact time with annual compounding next to the rule of 72:
| Annual rate | Exact years | Rule of 72 |
|---|---|---|
| 2 % | 35 | 36 |
| 4 % | 17.67 | 18 |
| 6 % | 11.9 | 12 |
| 8 % | 9.01 | 9 |
| 10 % | 7.27 | 7.2 |
| 12 % | 6.12 | 6 |
Frequently asked questions
What is compound interest?
It is interest figured on the starting amount and also on the interest already earned. Each period the base grows, so money grows faster and faster.
What is the difference between simple and compound interest?
Simple interest is figured only on the starting amount. Compound interest is figured on the starting amount plus past interest. With $10,000.00 at 5% for 10 years, simple interest reaches $15,000.00 and monthly compounding reaches $16,470.09.
Does it matter how often interest compounds?
Yes, but less than it seems. With $10,000.00 at 5% for 10 years, annual compounding gives $16,288.95 and continuous compounding gives $16,487.21. A higher rate or a longer term matters much more.
What is the effective annual rate?
It is the yearly rate that gives the same result as the stated rate with its compounding. A 5% rate compounded monthly equals an effective 5.1162% a year.
Is this calculator financial advice?
No. It is a math tool. Real rates change over time, and real accounts charge fees and taxes that are not included here.
Learn more
- Examples of exponential growth
- Applications of exponential functions
- Examples of geometric sequences
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