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?
$9,732
$7,924
$8,822
$8,848

Answer 1

To calculate the balance in the account at the end of 2 years using simple interest, we can use the formula:

\[
A = P + I
\]

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 interest rate (as a decimal)
- \( t \) is the time in years

Given:
- \( P = 7912 \)
- \( r = 5.75\% = 0.0575 \)
- \( t = 2 \)

Now, we can calculate the interest:

\[
I = 7912 \times 0.0575 \times 2
\]
\[
I = 7912 \times 0.115 = 910.88
\]

Next, we add the interest to the principal to find the total amount:

\[
A = 7912 + 910.88 = 8822.88
\]

Therefore, the balance in the account at the end of 2 years is approximately:

\[
A \approx 8823
\]

Among the options given, the amount closest to the balance is:

**$8,822**