Question
A deposit of $7,912 is made into a new account that earns 5.75% simple interest. No
additional deposits or withdrawals will be made for 2 years.
Which amount is closest to the balance in the account at the end of 2 years?
*Remember to use your STAAR Reference Sheet for support!
(1 point)
$9,732
$7,924
$8,822
$8,848
O
additional deposits or withdrawals will be made for 2 years.
Which amount is closest to the balance in the account at the end of 2 years?
*Remember to use your STAAR Reference Sheet for support!
(1 point)
$9,732
$7,924
$8,822
$8,848
O
Answers
GPT-4o mini
To calculate the total amount in the account after 2 years with simple interest, you can use the formula:
\[
A = P(1 + rt)
\]
where:
- \( A \) is the total amount after time \( t \),
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.
Given:
- \( P = 7,912 \)
- \( r = 5.75\% = 0.0575 \)
- \( t = 2 \)
Now plug these values into the formula:
\[
A = 7,912(1 + 0.0575 \times 2)
\]
Calculating the interest portion:
\[
0.0575 \times 2 = 0.115
\]
Now, substitute this back into the formula:
\[
A = 7,912(1 + 0.115)
\]
\[
A = 7,912(1.115)
\]
\[
A \approx 8,826.78
\]
Rounding to the nearest dollar, the amount is approximately \( 8,827 \).
The closest option provided is **$8,822**.
\[
A = P(1 + rt)
\]
where:
- \( A \) is the total amount after time \( t \),
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the time in years.
Given:
- \( P = 7,912 \)
- \( r = 5.75\% = 0.0575 \)
- \( t = 2 \)
Now plug these values into the formula:
\[
A = 7,912(1 + 0.0575 \times 2)
\]
Calculating the interest portion:
\[
0.0575 \times 2 = 0.115
\]
Now, substitute this back into the formula:
\[
A = 7,912(1 + 0.115)
\]
\[
A = 7,912(1.115)
\]
\[
A \approx 8,826.78
\]
Rounding to the nearest dollar, the amount is approximately \( 8,827 \).
The closest option provided is **$8,822**.