Final answer:
Ava will have $1,409.92 in her savings account at the second bank in 5 years.
Step-by-step explanation:
To calculate the future value of Ava's savings account with quarterly compounding, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where FV is the future value, P is the principal amount (initial deposit), r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Using the information given, we have: P = $1,300, r = 8.2% = 0.082, n = 4 (quarterly compounding), and t = 5.
Plugging these values into the formula, we get:
FV = $1,300(1 + 0.082/4)^(4*5)
FV = $1,409.92
Therefore, Ava will have $1,409.92 in her savings account at the second bank in 5 years.