Final answer:
After calculating compound interest separately for the first year with half-yearly compounding and the second year with yearly compounding, the interest earned on Rs 20,000 after two years at a 20% annual rate is Rs 9,040, which means none of the given options are correct.
Step-by-step explanation:
To calculate the interest earned on Rs 20,000 after two years with the given interest rate compounded differently across the two years, we need to use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
First year (compounded half-yearly): P = Rs 20,000, r = 20% or 0.20, n = 2, t = 1
A1 = 20000(1 + 0.20/2)^(2*1) = 20000(1 + 0.10)^2 = 20000(1.21) = Rs 24,200
Second year (compounded yearly): P = Rs 24,200 (new principal), r = 20% or 0.20, n = 1, t = 1
A2 = 24200(1 + 0.20/1)^(1*1) = 24200(1.20) = Rs 29,040
The interest earned at the end of two years will be the final amount minus the original principal: Rs 29,040 - Rs 20,000 = Rs 9,040.
Therefore, none of the options provided (a. Rs 4,800, b. Rs 4,928, c. Rs 5,120 or d. Rs 5,200) are correct.