Final answer:
The expression to calculate the interest charged for the billing cycle is (Average daily balance x APR x Number of days in billing cycle) / 365. Given the balances and APR, the interest charged for Sergei is $0.76.
Step-by-step explanation:
To calculate the amount Sergei was charged in interest for the billing cycle, we need to find the average daily balance and multiply it by the APR and the number of days in the billing cycle. The expression that can be used is:
Interest = (Average daily balance x APR x Number of days in billing cycle) / 365
Given that Sergei's balance for the first 12 days was $350 and for the last 18 days was $520, we can find the average daily balance by adding these balances and dividing by 30 (the total number of days in the billing cycle):
Average daily balance = (350 + 520) / 30 = $29
Substituting this value along with the APR of 14% and the number of days in the billing cycle into the expression:
Interest = (29 x 0.14 x 30) / 365
Interest = $0.76