Present Value of Annuity

The present value of an annuity is the present value of a series of equal payments made at equal intervals of time. It is used to determine the current value of a stream of equal payments made in the future.

Formula for Present Value of Annuity

The formula for present value of annuity is:

PV = (PMT x [1 - (1 + r)^-n]) / r

Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods

Calculating Present Value of Annuity

Given: PMT = Rs 1000, n = 10 years, r = 6%

Using the formula:

PV = (1000 x [1 - (1 + 0.06)^-10]) / 0.06
PV = 1000 x (6.7101) / 0.06
PV = Rs 67101

Therefore, the present value of the annuity is Rs 67101.

Explanation

The present value of an annuity is the sum of the present values of each payment. The present value of a single payment is the amount that would have to be invested today to grow to the future value of the payment at the given interest rate.

In this case, we have a series of equal payments of Rs 1000, made at the end of each year for 10 years. We want to determine the present value of this annuity at a 6% compounded interest rate.

Using the formula for present value of annuity, we can calculate that the present value of the annuity is Rs 67101. This means that if we were to invest Rs 67101 today at a 6% compounded interest rate, it would grow to Rs 1000 at the end of each of the next 10 years.