To calculate the total amount and total interest after eight months, we first need to calculate the interest rate per four months, as the interest is compounded every four months.
Interest rate per four months = (30% per annum)/3 = 10% per four months
Number of times the interest is compounded in eight months = 8/4 = 2
Using the formula for compound interest, we can calculate the total amount and total interest as follows:
Total amount = Principal x (1 + (rate/n))^nt
where:
Principal = 5000
rate = 30% per annum = 10% per four months
n = 4 (interest is compounded every four months)
t = 2 (two four-month periods in eight months)
Total amount = 5000 x (1 + (0.10/4))^2*4 = 5000 x (1.025)^8 = 7107.47
Therefore, the total amount after eight months is 7107.47.
Total interest = Total amount - Principal = 7107.47 - 5000 = 2107.47
Therefore, the total interest after eight months is 2107.47.