Forrest deposited $1,000 in a savings account that pays 5.5% interest,

compounded monthly. What was his balance at the end of the second
month after the interest had been added?

After one month, the interest earned would be:

1000 * (0.055/12) = $4.58

So after the first month, the balance would be:

1000 + 4.58 = $1,004.58

For the second month, we need to calculate the interest earned on this new balance:

1004.58 * (0.055/12) = $4.63

So after the second month, the balance would be:

1004.58 + 4.63 = $1,009.21

Therefore, Forrest's balance would be $1,009.21 at the end of the second month after the interest had been added.