To calculate the interest earned on Emma's deposit with an annual interest rate of 3% compounded annually, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial deposit or investment).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
In Emma's case:
- \( P = 500 \)
- \( r = 0.03 \) (3% as a decimal)
- \( n = 2 \)
Plugging in the values:
\[ A = 500(1 + 0.03)^2 \] \[ A = 500(1.03)^2 \] \[ A = 500 \times 1.0609 \] \[ A = 530.45 \]
Now, to find the interest earned, subtract the principal from the total amount:
\[ \text{Interest} = A - P \] \[ \text{Interest} = 530.45 - 500 = 30.45 \]
Therefore, after 2 years, Emma will have earned $30.45 in interest.
4 answers