The compound interest on $12,600 for 2 years at an annual rate of 10% is $2,646.
Understanding Compound Interest
Compound interest is the interest calculated on the initial principal and also on the accumulated interest from previous periods. It's often referred to as "interest on interest," leading to faster growth of an investment or debt compared to simple interest.
The Compound Interest Formula
To calculate compound interest (CI), we first determine the future value of the investment or loan and then subtract the original principal. The formula used for calculating the total amount (A) after compound interest is:
A = P (1 + R/100)T
Where:
- A = Amount (total principal and interest)
- P = Principal amount (the initial sum of money)
- R = Annual interest rate (as a percentage)
- T = Time the money is invested or borrowed for (in years)
Once the total amount (A) is calculated, the compound interest (CI) is found by:
CI = A - P
Step-by-Step Calculation
Let's calculate the compound interest for the given values:
- Principal (P): $12,600
- Rate (R): 10% per annum
- Time (T): 2 years
Here’s how the calculation unfolds:
-
Identify the variables:
- P = $12,600
- R = 10%
- T = 2 years
-
Apply the formula for the Amount (A):
- A = 12600 (1 + 10/100)²
- A = 12600 (1 + 0.10)²
- A = 12600 (1.10)²
- A = 12600 * 1.21
- A = 15246
-
Calculate the Compound Interest (CI):
- CI = A - P
- CI = 15246 - 12600
- CI = 2646
Therefore, the compound interest is $2,646.
Summary of Calculation
For clarity, here's a table summarizing the inputs and the calculated results:
| Item | Value |
|---|---|
| Principal (P) | $12,600 |
| Annual Rate (R) | 10% |
| Time (T) | 2 years |
| Total Amount (A) | $15,246 |
| Compound Interest (CI) | $2,646 |
Importance of Compound Interest
Compound interest is a fundamental concept in finance, crucial for understanding:
- Savings and Investments: How your money can grow significantly over time.
- Loans and Debt: How interest can accumulate rapidly, increasing the total amount owed.
- Financial Planning: It helps individuals and businesses make informed decisions about long-term financial goals, retirement planning, and debt management.
