Solution:

Given,
Payment (P) = Rs. 500
Time (n) = 4 years
Rate of interest (r) = 6% compounded quarterly

To find the future value of the annuity, we can use the formula:

FV = P * [(1 + r/4)^(4*n/3) - 1]/(r/4)

Here, we have quarterly payments and quarterly compounding, so we can directly use the formula.

Calculation:

FV = 500 * [(1 + 0.06/4)^(4*4/3) - 1]/(0.06/4)
FV = 500 * [1.015^5.33 - 1]/0.015
FV = 500 * 6.238/0.015
FV = 206,933.33 (approx)

Therefore, the future value of the annuity is Rs. 206,933.33.

Explanation:

The annuity consists of payments made at the end of every 3 months for 4 years.
This means there are a total of 16 payments (4 years * 4 quarters per year).
The rate of interest is 6% compounded quarterly.

To find the future value of the annuity, we use the formula mentioned above.
The formula calculates the future value of a series of periodic payments made at regular intervals, with compound interest.

The formula takes into account the payment amount, the time period, the interest rate, and the compounding frequency.
We plug in the values of payment, time, and rate in the formula and calculate the future value of the annuity.

In this case, the future value of the annuity is Rs. 206,933.33.
This means that if the payments of Rs. 500 are made at the end of every 3 months for 4 years with a rate of interest of 6% compounded quarterly, the total future value of the annuity will be Rs. 206,933.33.

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