How to use the compound interest calculator
- Enter the initial investment amount (if any)
- Enter the interest rate and select the period (monthly or annual)
- Optionally, add periodic contributions that will be made each period
- Enter the number of periods you want to simulate
- Click 'Calculate' to see the final value, interest earned, and growth chart
What are compound interest?
Compound interest is interest calculated on the initial amount plus accumulated interest from previous periods. Unlike simple interest, where interest is calculated only on the initial amount, compound interest makes money grow exponentially over time.
It's the concept behind 'interest on interest' and is considered one of the most powerful forces in the financial universe. The longer you leave money invested, the greater the effect of compound interest.
Compound interest is widely used in investments such as savings accounts, CDB, Treasury bonds, stocks, and other financial products that yield over time.
Compound interest formula
The basic compound interest formula is:
Basic formula (without contributions):
M = C × (1 + i)ⁿ
Where M is the final amount, C is the initial capital, i is the interest rate per period, and n is the number of periods. The rate and period must be in the same unit (both monthly or both annual).
With periodic contributions:
When there are periodic contributions, the calculation is more complex. Each period, you add the contribution and calculate interest on the accumulated total. The calculator does this automatically for you.
The formula with periodic contributions considers that each contribution also earns compound interest from the period it's made.
Simple vs compound interest
Understand the fundamental difference between the two types of interest:
Simple Interest
M = C × (1 + i × n)
Interest is calculated only on the initial capital. Growth is linear and slower. Used in some loans and specific situations.
Compound Interest
M = C × (1 + i)ⁿ
Interest is calculated on the initial capital plus accumulated interest. Growth is exponential and much faster over time. Used in most investments.
The difference between simple and compound interest increases exponentially with time. For long-term investments, compound interest makes a huge difference in the final accumulated value.
Rule of 72
The Rule of 72 is a quick way to estimate how long it takes to double an investment with compound interest:
Formula:
Time to double = 72 ÷ Annual interest rate
Divide 72 by the annual interest rate to find approximately how many years are needed to double the investment.
Example 1: With 6% per year: 72 ÷ 6 = 12 years to double
Example 2: With 12% per year: 72 ÷ 12 = 6 years to double
Example 3: With 24% per year: 72 ÷ 24 = 3 years to double
Periodic contributions and the power of compound interest
Making regular periodic contributions is one of the best strategies to take advantage of compound interest:
Advantages of periodic contributions:
- You invest regularly, taking advantage of average prices over time
- Each contribution also earns compound interest from the moment it's made
- Wealth growth is accelerated by the combination of contributions + compound interest
Practical example:
Investing R$ 1,000 initial + R$ 500/month at 1% per month for 10 years results in much more than investing only R$ 1,000 initial without contributions. Periodic contributions multiply the power of compound interest.
Practical example
Let's calculate a real investment:
Scenario:
- Initial amount: R$ 10,000
- Interest rate: 1% per month (12% per year)
- Monthly contributions: R$ 500
- Period: 10 years (120 months)
- Selected period: Monthly
Expected results:
- Total contributions: R$ 60,000 (R$ 500 × 120 months)
- Interest earned: approximately R$ 50,000+
- Final value: approximately R$ 120,000+
- The chart shows month-by-month evolution, showing how compound interest accelerates growth over time
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Important notice
This calculator is educational and provides estimates based on entered data. Results may vary due to factors such as changes in interest rates, specific investment conditions, taxes on earnings, administrative fees not considered, and other external factors. Use results as an analysis tool and consult financial professionals for important decisions.