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 with a deposit earning simple interest, you can use the formula for simple interest:

\[
A = P + I
\]

Where:
- \( A \) is the total amount in the account after time \( t \)
- \( P \) 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)
- \( t \) is the time the money is invested or borrowed for, in years

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

First, calculate the interest:

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

\[
I = 7,912 \times 0.0575 = 454.06 \quad (\text{approx.})
\]

Now multiplying by 2 for 2 years:

\[
I = 454.06 \times 2 = 908.12 \quad (\text{approx.})
\]

Now add the interest to the principal to find the total amount:

\[
A = P + I = 7,912 + 908.12 \approx 8,820.12
\]

Now looking at the answer choices, the closest amount to the calculated balance of approximately $8,820.12 is:

**$8,822**