Compound Interest Calculator
Calculation Results
" + "Future Value: $" + futureValue.toFixed(2) + "" + "Total Interest Earned: $" + totalInterestEarned.toFixed(2) + ""; }Understanding Compound Interest
Compound interest is often called the "eighth wonder of the world" because of its power to grow wealth over time. Unlike simple interest, which is calculated only on the initial principal amount, compound interest is calculated on the initial principal plus the accumulated interest from previous periods. This means your money starts earning money on itself, leading to exponential growth.
How it Works
The core principle of compound interest is that interest is added to the principal, and then the next interest calculation is based on this new, larger principal. This snowball effect can significantly boost your investment returns over the long term.
The Formula
The formula used in this calculator is the standard compound interest formula:
A = P (1 + r/n)^(nt)
Where:
Ais the future value of the investment/loan, including interestPis the principal investment amount (the initial deposit or loan amount)ris the annual interest rate (as a decimal)nis the number of times that interest is compounded per yeartis the number of years the money is invested or borrowed for
In our calculator, we adapt this slightly for ease of use:
- We ask for the annual interest rate as a percentage, so we divide by 100 in the calculation.
ratePerPeriod (r/n)represents the interest rate for each compounding period.numberOfPeriods (nt)represents the total number of times interest will be compounded over the investment's life.
Key Factors Influencing Compound Interest
- Principal Amount: The larger your initial investment, the more significant the compounding effect will be.
- Interest Rate: A higher interest rate leads to faster growth. Even small differences in rates can have a big impact over time.
- Time Horizon: The longer your money is invested, the more time it has to compound. This is why starting early is crucial for long-term investments like retirement planning.
- Compounding Frequency: Interest compounded more frequently (e.g., monthly vs. annually) will result in slightly higher returns due to the interest being added and earning interest more often.
Example Calculation
Let's say you invest an initial principal of $10,000 with an annual interest rate of 5% for 20 years. If the interest is compounded monthly (12 times per year):
- Principal (P): $10,000
- Annual Interest Rate (r): 5% (or 0.05)
- Number of Years (t): 20
- Compounding Frequency (n): 12
Using the calculator with these inputs:
- Rate per period = (0.05 / 12) ≈ 0.00416667
- Number of periods = 20 * 12 = 240
- Future Value = $10,000 * (1 + 0.00416667)^240 ≈ $27,126.40
- Total Interest Earned = $27,126.40 – $10,000 = $17,126.40
This example demonstrates how your initial $10,000 could grow to over $27,000, with more than half of that being earned through compound interest!