Answer: The compound interest on a savings account is calculated by multiplying the principal (initial amount deposited) by the interest rate, and then multiplying that result by the number of compounding periods.
In this case, the principal is $925, the interest rate is 5.5%, and the number of compounding periods is 2 (since the interest is compounded semiannually).
To calculate the compound interest, we can use the following formula:
Compound interest = principal * (1 + interest rate/number of compounding periods)^(number of compounding periods * number of years) - principal
Plugging in the values from the problem, we get:
Compound interest = $925 * (1 + 5.5%/2)^(2 * 1) - $925
= $925 * 1.0275^2 - $925
= $925 * 1.056 - $925
= $973.44 - $925
= $48.44
Therefore, the compound interest on Matthew's savings account is $48.44.