We can solve this using the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
Substituting the given values:
P = $7,873
r = 6% = 0.06
n = 2 (compounded 2 times per year)
t = 4
A = $7,873(1 + 0.06/2)^(2 * 4)
A = $10,340.47
Therefore, the account balance will be $10,340.47 after 4 years.