Final answer:
The total amount earned after 5 years in a bank account with 5000AED compounded at 8% and two plans of annual or semiannual compounding is approximately 6655.93 AED for the annual compounding plan and 6853.50 AED for the semiannual compounding plan.
Step-by-step explanation:
To calculate the total amount earned, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the total amount, P is the initial amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the initial amount is 5000AED, the interest rate is 8%, and the bank offers two plans: annual compounding and semiannual compounding. For the annual compounding plan, n = 1. Plugging the values into the formula, we get A = 5000(1 + 0.08/1)^(1*5) = 5000(1.08)^5. For the semiannual compounding plan, n = 2. Plugging the values into the formula, we get A = 5000(1 + 0.08/2)^(2*5) = 5000(1.04)^10. Calculating the values, the total amount earned after 5 years in both cases would be approximately 6655.93 AED for the annual compounding plan and 6853.50 AED for the semiannual compounding plan.