If the payment of ₹2,000 is made at the end of every quarter for 10 years at the rate of 8% per year, then find the amount of annuity.

To calculate the amount of annuity, we can use the formula for the future value of an ordinary annuity:

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

where:

• FV is the future value of the annuity
• P is the payment per period (₹2,000 in this case)
• r is the annual interest rate (8% or 0.08 in this case)
• n is the number of compounding periods per year (4 in this case, because payments are made quarterly)
• t is the number of years (10 in this case)

Substituting the given values into the formula, we get:

FV = 2000 * [(1 + 0.08/4)^(4*10) - 1] / (0.08/4)

Now, calculate the expression in the brackets:

(1 + 0.08/4)^(4*10) - 1 = (1 + 0.02)^40 - 1 ≈ 2.20804 - 1 = 1.20804

Then, divide this by the quarterly interest rate:

1.20804 / (0.08/4) = 1.20804 / 0.02 = 60.402

Finally, multiply this by the payment per period:

FV = 2000 * 60.402 = ₹1,208,040

So, the amount of the annuity after 10 years would be approximately ₹1,208,040.