Question

Ariana has $1000 to put in a savings account. she is choosing between two banks. bank a offers 7% compounded quarterly and bank b offers 7.1% compounded semiannually. if ariana plans on keeping her money in a savings account for a year, which bank would pay her more in interest, and by how much? a. bank b by 40 cents b. bank a by 40 cents c. bank a by 33 cents d. bank b by 33 cents

Answer 1

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:

1. Bank A: A = 1000(1 + 0.07/4)⁴ˣ¹ = $1072.02
2. 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.

Answer 2

Bank B will pay Ariana more in interest by $0.20.

Explanation:To determine which bank will pay Ariana more interest, we need to calculate the total amount she will have in each bank after one year. Bank A offers 7% compounded quarterly, which means that the interest is added to the account four times a year. Bank B offers 7.1% compounded semiannually, which means that the interest is added to the account two times a year.

Using the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the final amount

P = the principal (initial amount)

r = the interest rate (expressed as a decimal)

n = the number of times interest is compounded per year

t = the number of years

For Bank A:

A = 1000(1 + 0.07/4)^(4*1) = 1000(1.0175)^4 ≈ 1000(1.0709) ≈ $1070.90

For Bank B:

A = 1000(1 + 0.071/2)^(2*1) = 1000(1.0355)^2 ≈ 1000(1.0711) ≈ $1071.10

Bank B will pay Ariana more in interest by $0.20 (approximately). Therefore, the correct answer is Bank B by 20 cents.