To calculate the compound interest, you can use the formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
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 time the money is invested for in years.
In this case:
- \( P = 5000 \)
- \( r = 0.10 \) (10% as a decimal)
- \( n = 1 \) (compounded annually)
- \( t = 2 \)
Plugging in the values:
\[ A = 5000 \left(1 + \frac{0.10}{1}\right)^{1 \cdot 2} \]
This simplifies to:
\[ A = 5000 \left(1 + 0.10\right)^{2} \] \[ A = 5000 \left(1.10\right)^{2} \] \[ A = 5000 \times 1.21 \] \[ A = 6050 \]
Now, to find the compound interest, subtract the principal from the total amount:
\[ \text{Compound Interest} = A - P = 6050 - 5000 = 1050 \]
Thus, the compound interest on $5000 for 2 years at 10% per annum is $1050.