After 3 years with daily compounding at 11%, the $400 investment will grow to approximately $578.51.
Calculate the daily interest rate:
Divide the annual rate by the number of compounding periods per year (365 days in this case).
Daily rate = 11% / 365 = 0.0298765%.
Determine the total number of compounding periods:
Multiply the number of years by the number of compounding periods per year.
Total periods = 3 years * 365 days/year = 1095 days.
Use the compound interest formula:
A = P * (1 + r)^n, where:
A is the final amount
P is the initial principal (400 dollars)
r is the daily interest rate (0.0298765%)
n is the total number of compounding periods (1095 days)
Plug in the values and calculate:
A = 400 * (1 + 0.000298765)^1095 = 578.5090 dollars (approximately)