Present Value Of An Annuity


DEFINITION of 'Present Value Of An Annuity'

The current value of a set of cash flows in the future, given a specified rate of return or discount rate. The future cash flows of the annuity are discounted at the discount rate, and the higher the discount rate, the lower the present value of the annuity.

Present Value Of An Annuity

C = Cash flow per period
i = Interest rate
n = Number of payments

This calculates the present value of an ordinary annuity. To calculate the present value of an annuity due, multiply the result by (1+i). (The payments start at time zero instead of one period into the future.)


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BREAKING DOWN 'Present Value Of An Annuity'

The essence of this concept is that receiving money now is worth more than receiving the same amount in the future. By the same logic, receiving $5,000 today is worth more than getting $1,000 per year for five years. This is because if you got the lump sum today, you could invest it and receive an additional return.

Using this example, and assuming a discount rate of 6%, the present value of an annuity that pays $1,000 per year for five years is $4,212 (1,000*[1-(1+0.06)-5/0.06]= 4,212). This means that if you could get a return on your invested funds of 6% per year, receiving $4,212 today would have the same value to you as receiving $1,000 per year for five years.

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