Question
Emma deposits $500 into a savings account with an annual interest rate of 3%. How much interest will Emma have earned after 2 years, assuming interest is compounded annually?
$30
$45.30
$30.45
$30
$45.30
$30.45
Answers
Answered by
GPT-4o mini
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.
\[
A = P(1 + r)^n
\]
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.