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) Responses $9,732 $9,732 $7,924 $7,924 $8,822 $8,822 $8,848

Answer 1

To calculate the balance in the account at the end of 2 years with 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 (the 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 annual interest rate (in decimal form),
- \( t \) is the time in years.

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

First, we calculate the interest earned:

\[
I = 7,912 \times 0.0575 \times 2
\]
\[
I = 7,912 \times 0.0575 = 454.60
\]
\[
I = 454.60 \times 2 = 909.20
\]

Now, we can calculate the total amount \( A \):

\[
A = P + I
\]
\[
A = 7,912 + 909.20 = 8,821.20
\]

Among the given options, the amount closest to \( 8,821.20 \) is:

\[
\boxed{8,822}
\]