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 simple interest, we 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 annual interest rate (expressed as a decimal),
- \( t \) is the time in years.

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

First, calculate the interest:

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

Calculating \( 7,912 \times 0.0575 \):

\[
7,912 \times 0.0575 = 454.06
\]

Now, multiplying by 2 for the 2 years:

\[
I = 454.06 \times 2 = 908.12
\]

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

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

The closest amount to the balance in the account after 2 years is:

\[
\boxed{8,822}
\]