Compound Interest Calculator
Understanding Compound Interest
Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. It's often referred to as "interest on interest." This concept is fundamental to understanding how investments grow over time and how debt can accumulate rapidly.
How Compound Interest Works
The magic of compound interest lies in its exponential growth potential. Unlike simple interest, where interest is only calculated on the original principal amount, compound interest reinvests the earned interest back into the principal. This larger principal then earns more interest in the next period, creating a snowball effect.
The formula for compound interest is:
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
Key Components of the Formula
- Principal (P): This is the initial sum of money you start with. In our calculator, this is the "Principal Amount ($)".
- Interest Rate (r): This is the rate at which your money grows per year. In our calculator, this is the "Annual Interest Rate (%)". Remember to convert this percentage to a decimal for calculations (e.g., 5% becomes 0.05).
- Compounding Frequency (n): This refers to how often the interest is calculated and added to the principal within a year. Common frequencies include annually (n=1), quarterly (n=4), monthly (n=12), and daily (n=365). Our calculator uses the "Compounding Frequency (per year)" dropdown.
- Time (t): This is the duration for which the money is invested or borrowed, measured in years. In our calculator, this is the "Number of Years".
Why Compound Interest Matters
Compound interest is a powerful tool for wealth building. By starting early and allowing your investments to compound over extended periods, you can significantly increase your returns. Even small amounts invested regularly can grow substantially thanks to this effect.
Conversely, compound interest can work against you with debt. High-interest debts that are not paid off quickly can escalate rapidly due to compounding, making them difficult to manage.
Example Calculation
Let's say you invest $1,000 (Principal) at an annual interest rate of 5% (Interest Rate). If the interest is compounded monthly (Compounding Frequency) for 10 years (Number of Years):
- P = $1,000
- r = 5% or 0.05
- n = 12 (monthly compounding)
- t = 10 years
Using the formula A = P (1 + r/n)^(nt):
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 investment of $1,000 would grow to approximately $1,647.01 after 10 years, with $647.01 being the accumulated compound interest.