We can use the formula for compound interest to solve this problem:
A = P (1 + r/n)^(nt)
where:
A = final amount
P = principal (initial deposit)
r = annual interest rate (as a decimal)
n = number of times compounded per year
t = time elapsed (in years)
In this case, we know that the account has been open for 2 years, and that the interest is compounded quarterly (i.e., n = 4). We also know that the current balance is $500.00. We can use these values to solve for the initial deposit, P:
500 = P (1 + 0.08/4)^(4*2)
Simplifying the right-hand side:
500 = P (1.02)^8
Dividing both sides by (1.02)^8:
500 / (1.02)^8 = P
P ≈ $414.09
Therefore, Leah initially deposited approximately $414.09 into the savings account.