J is considering two investment option to invest Ts1000000/=.option A offers an interest rate of 6%annually while option B offer 5% semiannually. What is the best options to be invested after 5 years?

To determine the best option, we need to calculate the future value of the investments after 5 years.

Option A:
The formula to calculate the future value of an investment with compound interest is:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (initial investment)
r = interest rate per period
n = number of compounding periods per year
t = number of years

In this case, PV = Ts1000000, r = 6% = 0.06, n = 1 (annually), and t = 5.
FV_A = Ts1000000 * (1 + 0.06/1)^(1*5)
FV_A = Ts1000000 * (1.06)^5
FV_A = Ts1000000 * 1.3382255776
FV_A = Ts1,338,225.58

Option B:
Since the interest is compounded semiannually, we need to adjust the interest rate and the number of compounding periods.
The interest rate per period would be 5% / 2 = 0.05/2 = 0.025
The number of compounding periods would be 2 * 5 = 10 (twice per year for 5 years)

Using the same formula as above:
FV_B = Ts1000000 * (1 + 0.025/1)^(1*10)
FV_B = Ts1000000 * (1.025)^10
FV_B = Ts1000000 * 1.2800840321
FV_B = Ts1,280,084.03

Comparing the future values, we can see that Option A has a higher value after 5 years (Ts1,338,225.58) compared to Option B (Ts1,280,084.03). Therefore, Option A is the better investment option.