Final answer:
The balance of the account at the end of the three-year period is approximately $8,638.46. The amount of interest earned is $638.46. The effective rate of interest is approximately 3.5700%.
Step-by-step explanation:
To find the balance of the account at the end of the period, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the balance at the end, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, P = $8000, r = 3.5% (or 0.035), n = 365, and t = 3. Plugging these values into the formula, we get:
A = 8000(1 + 0.035/365)^(365*3)
Calculating this using a calculator or a computer program, we find that the balance at the end of the period is approximately $8,638.46.
To find the amount of interest earned, we subtract the principal amount from the balance: 8,638.46 - 8000 = $638.46.
The effective rate of interest is the annual rate of interest that would yield the same amount of interest if the interest were simple interest. To find it, we can use the formula: Effective rate = (1 + r/n)^(n) - 1, where r is the annual interest rate and n is the number of times interest is compounded per year. Plugging in the values r = 0.035 and n = 365, we get:
Effective rate = (1 + 0.035/365)^(365) - 1
Calculating this, we find that the effective rate of interest is approximately 3.5700%.