Final answer:
The total amount in the compound interest account is approximately $11537.34
Step-by-step explanation:
To find the total amount in the compound interest account, we can use the formula A = P(1 + r/n)^(nt), where A is the total 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, the principal amount is $5550, the annual interest rate is 10%, and the interest is compounded semiannually, so n = 2. The number of years is 13.
Substituting these values into the formula:
A = 5550(1 + 0.1/2)^(2*13)
Simplifying:
A = 5550(1.05)^(26)
Calculating the value of (1.05)^26:
(1.05)^26 ≈ 2.07793
Now, multiply the principal amount by the value we just calculated:
A ≈ 5550 * 2.07793
Therefore, the total amount in the compound interest account is approximately $11537.34.