Compound Interest Calculator
Understanding Compound Interest
Compound interest, often called "interest on interest," is a powerful concept in finance that allows your investments to grow exponentially over time. Unlike simple interest, which is calculated only on the initial principal amount, compound interest is calculated on the principal plus any accumulated interest from previous periods. This means your earnings start generating their own earnings, leading to a snowball effect.
How it Works:
The magic of compounding lies in its cyclical nature. At each compounding period (e.g., annually, monthly, daily), the interest earned is added to the principal. In the next period, interest is then calculated on this new, larger sum. The more frequently interest is compounded, the faster your investment will grow, assuming all other factors remain the same.
The Formula:
The future value of an investment with compound interest can be calculated using the following formula:
$A = P (1 + r/n)^(nt)$
Where:
- $A$ = the future value of the investment/loan, including interest
- $P$ = the principal investment amount (the initial deposit or loan amount)
- $r$ = the annual interest rate (as a decimal)
- $n$ = the number of times that interest is compounded per year
- $t$ = the number of years the money is invested or borrowed for
Example Calculation:
Let's say you invest $1,000 (P) with an annual interest rate of 5% (r = 0.05). You plan to leave it invested for 10 years (t) and the interest is compounded monthly (n = 12). Using the formula:
$A = 1000 * (1 + 0.05/12)^(12*10)$ $A = 1000 * (1 + 0.00416667)^(120)$ $A = 1000 * (1.00416667)^(120)$ $A = 1000 * 1.647009$ $A ≈ $1,647.01$
This means your initial $1,000 investment would grow to approximately $1,647.01 after 10 years, with $647.01 being the earned compound interest.
Why it Matters:
Understanding and utilizing compound interest is crucial for long-term financial goals like retirement planning, saving for a down payment, or even understanding the cost of debt. Starting early and compounding consistently can significantly impact your wealth accumulation over time.