To calculate the balance after 4 years, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the balance after t years
P is the principal amount (the initial deposit)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time in years
In this problem, we have:
P = $6000
r = 11% = 0.11
n = 365 (daily compounding)
t = 4 years
Let's plug in the values and solve for A:
A = 6000 * (1 + 0.11/365)^(365*4)
A = $10,874.36 (rounded to two decimal places)
Therefore, the balance after 4 years is approximately $10,874.36.