Final answer:
Bank B pays Ariana more interest by $0.49.
Step-by-step explanation:
To calculate the interest earned by each bank, we can use the formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (initial amount), r is the annual interest rate (written as a decimal), n is the number of times interest is compounded per year, and t is the number of years.
In Bank A, the principal is $1000, the annual interest rate is 7% (or 0.07), and interest is compounded quarterly (n = 4).
In Bank B, the principal is $1000, the annual interest rate is 7.1% (or 0.071), and interest is compounded semiannually (n = 2).
Using the formula, we can calculate the amount in each bank after one year:
- Bank A: A = 1000(1 + 0.07/4)⁴ˣ¹ = $1072.02
- Bank B: A = 1000(1 + 0.071/2)²ˣ¹) = $1072.51
Bank B pays Ariana more interest by $1072.51 - $1072.02 = $0.49. Therefore, the correct answer is d. bank b by 49 cents.