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?

Answer 1

To calculate the total balance in an account after earning simple interest, we use the formula:

\[
A = P(1 + rt)
\]

where:
- \( A \) is the total amount in the account after time \( t \),
- \( P \) is the principal amount (initial deposit),
- \( r \) is the rate of interest (as a decimal),
- \( t \) is the time in years.

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

Now plug the values into the formula:

\[
A = 7912 \left(1 + (0.0575 \times 2)\right)
\]

Calculating the interest part:

\[
0.0575 \times 2 = 0.115
\]

Adding this to 1:

\[
1 + 0.115 = 1.115
\]

Now substitute back into the formula:

\[
A = 7912 \times 1.115
\]

Calculating this gives:

\[
A \approx 8817.58
\]

Rounding this to the nearest dollar, the balance in the account at the end of 2 years is approximately:

\[
\boxed{8818}
\]