Final answer:
To find the total amount in a compound interest account, we can use the formula A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Step-by-step explanation:
To find the total amount in a compound interest account, we can use the formula A = P(1 + r/n)^(nt), where A is the future amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, we have a principal amount of $5750, an annual interest rate of 12%, and interest is compounded semiannually. So n = 2 and t = 12. Plugging these values into the formula, we get A = 5750(1 + 0.12/2)^(2*12) = 5750(1 + 0.06)^24.
Calculating this expression, we find A is approximately $17,705.20. So the total amount in the compound interest account is $17,705.20.