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)

3 \$9,732

S 7,924

O $8,822

$8,848

Answer 1

To calculate the balance in an account that earns simple interest, you can use the formula for simple interest:

\[
A = P + I
\]

Where:
- \( A \) is the total amount in the account after interest.
- \( P \) is the principal amount (initial deposit).
- \( I \) is the interest earned.

The interest \( I \) can be calculated using the formula:

\[
I = P \times r \times t
\]

Where:
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.

Given:
- \( P = 7,912 \)
- \( r = 5.75\% = 0.0575 \)
- \( t = 2 \)

Now calculate the interest:

\[
I = 7,912 \times 0.0575 \times 2
\]

Calculating the interest:

\[
I = 7,912 \times 0.0575 = 455.06
\]
\[
I = 455.06 \times 2 = 910.12
\]

Now, add the interest to the principal to find the total amount \( A \):

\[
A = 7,912 + 910.12 = 8,822.12
\]

Rounding to the nearest cent (though it’s clear the options are whole), the balance in the account at the end of 2 years is approximately **$8,822**.

Thus, the closest amount to the balance in the account at the end of 2 years is:

**$8,822**.