Compound interest can be calculated using the formula:
\[ A = P (1 + r/n)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
To calculate the compound interest earned, you can subtract the principal from the total amount:
\[ \text{Compound Interest} = A - P \]
Steps to Calculate Compound Interest:
- Determine the principal amount (\( P \)).
- Specify the annual interest rate (\( r \)) and convert it to decimal form (e.g., 5% becomes 0.05).
- Decide how frequently the interest is compounded (e.g., annually, semi-annually, quarterly, monthly).
- Determine the time the money is invested or borrowed (\( t \)) in years.
- Plug the values into the formula to calculate \( A \).
- Subtract the principal (\( P \)) from \( A \) to find the compound interest.
Example:
Suppose you invest $1,000 (principal) at an annual interest rate of 5% (0.05) for 10 years, compounded annually (\( n = 1 \)).
- \( P = 1000 \)
- \( r = 0.05 \)
- \( n = 1 \)
- \( t = 10 \)
Plugging these values into the formula:
\[ A = 1000 \times (1 + 0.05/1)^{1 \times 10} = 1000 \times (1 + 0.05)^{10} = 1000 \times (1.05)^{10} \]
Calculating \( (1.05)^{10} \):
\[ (1.05)^{10} \approx 1.62889 \]
Now, calculate \( A \):
\[ A \approx 1000 \times 1.62889 \approx 1628.89 \]
Finally, to find the compound interest:
\[ \text{Compound Interest} = A - P = 1628.89 - 1000 \approx 628.89 \]
So, the compound interest earned over 10 years would be approximately $628.89.