A sum of Rs. 30000 invested in a scheme where the interest gets compounded annually and grows to Rs. 51840 in three years. How much interest in Rs. would have got accrued in six months in the same scheme had the interest been compounded quarterly?Question 6Answera.3075b.2975c.3024d.3126

First, let's find the annual interest rate using the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) n = number of times that interest is compounded per year t = time the money is invested for in years

Given in the problem: A = Rs. 51840 P = Rs. 30000 n = 1 (since it's compounded annually) t = 3 years

Substituting these values into the formula, we get:

51840 = 30000(1 + r/1)^(1*3)

Solving this equation for r, we get:

r = ((51840/30000)^(1/3)) - 1 r = 0.2 or 20%

Now, let's find out how much interest would have been accrued in six months if the interest was compounded quarterly.

Here, n = 4 (since it's compounded quarterly) and t = 0.5 (since it's for six months).

Using the formula for compound interest, we get:

A = P(1 + r/n)^(nt)

Substituting the values, we get:

A = 30000(1 + 0.2/4)^(4*0.5)

Calculating this, we get:

A = Rs. 30730.24

So, the interest accrued in six months would be A - P = 30730.24 - 30000 = Rs. 730.24

Therefore, none of the options (a.3075, b.2975, c.3024, d.3126) match the calculated interest.