Final answer:
The balance in the investment account after 12 years with compound interest can be calculated using the formula A = P(1 + r/n)^(nt). Plugging in the given values, the balance will be approximately $5,866.66.
Step-by-step explanation:
To calculate the balance in the investment account after 12 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the balance after t years
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
In this case, P is $4,000, r is 3.9% (or 0.039 as a decimal), n is 2 (since interest is compounded semi-annually), and t is 12. Plugging these values into the formula:
A = 4000(1 + 0.039/2)^(2*12)
After calculating, the balance in the account after 12 years will be approximately $5,866.66.