If $835 is invested in an account that earns annual interest of 4.5%, compounded semiannually, what will the account balance be after 13 years? (Round your answer to the nearest cent.)

To find the account balance after 13 years, compounded semiannually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the future value of the investment/total account balance
P = the principal/investment amount ($835)
r = the annual interest rate (4.5% or 0.045)
n = the number of times interest is compounded per year (2, since it is compounded semiannually)
t = the number of years (13)

Now, we can substitute the given values into the formula:

A = 835(1 + 0.045/2)^(2*13)

First, let's simplify the exponent part:

A = 835(1 + 0.0225)^(26)

Next, let's calculate the value inside the parentheses:

1 + 0.0225 = 1.0225

So, the equation becomes:

A = 835 * 1.0225^26

Now we will calculate the value of 1.0225^26:

1.0225^26 ≈ 1.6634

Finally, we can find the account balance by multiplying 835 by 1.6634:

A ≈ 835 * 1.6634 ≈ $1389.41

Therefore, the account balance will be approximately $1389.41 after 13 years.