Compound interest works by earning interest not only on your initial principal (the original amount of money saved or invested) but also on the interest that has been added to that principal from previous periods. This means your money grows faster over time because each period's interest is calculated on an increasingly larger amount, which includes prior interest earnings
. Here is how it works in practice:
- Suppose you deposit $1,000 at an annual interest rate of 10%. After the first year, you earn $100 in interest, making your total $1,100.
- In the second year, you earn 10% interest not just on the original $1,000 but on the entire $1,100, which equals $110 in interest. Your total is now $1,210.
- This process continues, with interest compounding on the new total each year, causing your savings to grow exponentially rather than linearly
The formula to calculate compound interest is:
Compound Interest=P×(1+i)n−P\text{Compound Interest}=P\times (1+i)^n-PCompound Interest=P×(1+i)n−P
Where:
- PPP = principal (initial amount)
- iii = interest rate per period
- nnn = number of compounding periods
For example, investing $10,000 at 5% interest compounded annually for 3 years results in:
10,000×(1+0.05)3−10,000=1,576.2510,000\times (1+0.05)^3-10,000=1,576.2510,000×(1+0.05)3−10,000=1,576.25
So, you earn $1,576.25 in interest over 3 years
. The frequency of compounding (daily, monthly, quarterly, yearly) affects how quickly the interest accumulates—the more frequent the compounding, the faster the growth
. Compound interest is powerful because it accelerates growth over time, especially when you leave your money invested and continue to add to it. This effect is often described as "interest on interest," and it can significantly increase your savings or investment value over the long term
. In summary, compound interest works by reinvesting earned interest so that future interest calculations include both the original principal and accumulated interest, leading to exponential growth of your money.
