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?
(1 point)
0 $9,732
• $7,924.
$8.822
$8,848

Answer 1

To calculate the balance in the account after 2 years with simple interest, use the formula for simple interest:

\[
A = P + I
\]

where:
- \( A \) is the total amount in the account after t years,
- \( P \) is the principal amount (initial deposit),
- \( I \) is the interest earned, calculated as:

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

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

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

First, calculate the interest:

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

Calculating the interest:

\[
I = 7,912 \times 0.0575 \times 2 = 7,912 \times 0.115 = 910.88
\]

Now, calculate the total amount in the account:

\[
A = P + I = 7,912 + 910.88 = 8,822.88
\]

Rounding to the nearest dollar gives us \( 8,823 \).

The closest amount to the balance in the account at the end of 2 years from the options provided is:

- **$8,822**.