Final answer:
The total account balance of the freelance artist's investment after 6 months, with a 3.05% annual interest compounded monthly, is $3,777.09, according to the compound interest formula. This corresponds to option c.
Step-by-step explanation:
The freelance artist invested $3,720 in a savings account earning 3.05% annual interest compounded monthly. The formula for compound interest is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years the money is invested for.
Applying the formula to this scenario for 6 months (or 0.5 years) with monthly compounding (n=12), we get:
A = 3720(1 + 0.0305/12)12*0.5
A = 3720(1 + 0.00254167)6
A = 3720(1.00254167)6
A = 3720(1.01531923)
A = $3,777.09
Therefore, the total account balance after 6 months is $3,777.09, which matches option c.