Final answer:
To find the time it will take for the account balance to reach $8,921.74, we can use the formula for compound interest and solve for time. Plugging in the values given and using logarithms, we find that it will take approximately 2.56 years for the account balance to reach the desired amount.
Step-by-step explanation:
To find the time it will take for the account balance to reach $8,921.74, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Here, A represents the final amount, P represents the initial amount, r represents the interest rate, n represents the number of times the interest is compounded per year, and t represents the time in years.
Plugging in the values into the formula, we have:
A = $8,921.74; P = $7,373; r = 0.0273 (2.73% as a decimal); n = 6
By rearranging the formula and solving for t, we can find:
t = log1 + r/n((A/P)) / n
Substituting in the values:
t = log1 + 0.0273/6((8,921.74/7,373)) / 6
t = log1 + 0.00455(1.21116) / 6
Using a calculator, we can find that t = 2.56
Therefore, it will take approximately 2.56 years for the account balance to reach $8,921.74.