Compound Interest Calculator
Calculate and visualize compound interest growth. Enter your principal amount, interest rate, time (in years, months, weeks, or days), and compounding frequency to see total value, interest earned, and effective annual rate with detailed graphs and yearly breakdowns.
Calculate Your Investment Growth
Calculation Explanation
Enter values above to see the step-by-step compound interest calculation.
Yearly Growth Breakdown
| Year | Principal | Interest | Cumulative Interest | Total |
|---|
What is Compound Interest?
Compound interest is the process of earning interest on both the initial principal and the interest accumulated over time. Unlike simple interest, which is calculated only on the principal, compound interest grows exponentially, making it a powerful tool for wealth building.
Key Formulas:
1. Compound Interest Formula
Where:
- \(A\) is the final amount (principal + interest).
- \(P\) is the principal amount.
- \(r\) is the annual interest rate (as a decimal).
- \(n\) is the number of times interest is compounded per year.
- \(t\) is the time in years.
2. Interest Earned
3. Effective Annual Rate
Compound interest is widely used in savings accounts, investments, loans, and financial planning to project future wealth or debt.
Frequently Asked Questions (FAQs)
1. What is compound interest?
Compound interest is interest earned on both the initial principal and the accumulated interest, leading to exponential growth over time.
2. How is compound interest calculated?
Use the formula \( A = P \left(1 + \frac{r}{n}\right)^{nt} \), where \( A \) is the final amount, \( P \) is the principal, \( r \) is the interest rate, \( n \) is the compounding frequency, and \( t \) is time in years.
3. What is the difference between simple and compound interest?
Simple interest is calculated only on the initial principal, while compound interest is calculated on the principal plus accumulated interest, leading to exponential growth.
4. Why does compounding frequency matter?
More frequent compounding (e.g., daily vs. annually) results in higher returns because interest is calculated and added to the principal more often.
5. What is the effective annual rate?
The effective annual rate (\( r_{\text{eff}} \)) is the actual annual interest rate when compounding is considered, calculated as \( r_{\text{eff}} = \left(1 + \frac{r}{n}\right)^n - 1 \).
6. How does time affect compound interest?
Longer time periods increase compound interest exponentially due to the \( nt \) term in the formula, leading to significant growth over time.
7. Can I use this calculator for loans?
Yes, this calculator can estimate loan growth by treating the loan amount as the principal and the interest rate as the borrowing rate.
8. What is a realistic interest rate to use?
Realistic rates depend on the investment type: savings accounts (0.5-2%), bonds (2-5%), or stocks (5-10% average historical returns).
9. What happens if I increase the principal amount?
A larger principal increases both the total amount and interest earned proportionally, as \( P \) is a multiplier in the formula.
10. Can I use this for daily compounding?
Yes, select "Daily" (n=365) in the compounding frequency dropdown to calculate daily compounding.
11. How accurate is this calculator?
The calculator uses precise mathematical formulas and is highly accurate for theoretical calculations, though real-world results may vary due to taxes or fees.
12. What are real-world applications of compound interest?
Compound interest applies to savings accounts, retirement funds, investment portfolios, and loan repayments, helping plan financial goals.
13. Does inflation affect compound interest?
Yes, inflation reduces the real value of returns. This calculator shows nominal growth; adjust the rate downward to account for inflation.
14. Can I use this for continuous compounding?
This calculator supports discrete compounding (e.g., daily, monthly). For continuous compounding, use the formula \( A = P e^{rt} \).
15. How do I interpret the growth chart?
The chart shows the investment’s total value (blue line) and interest earned (green line) over time, visualizing exponential growth.
16. What is the Rule of 72?
The Rule of 72 estimates the time to double an investment: \( \text{Time} \approx \frac{72}{\text{Interest Rate}} \). It’s an approximation for annual compounding.
17. Can I use this for retirement planning?
Yes, this calculator helps estimate retirement savings growth by inputting your initial savings, expected return rate, and time until retirement.
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