A perpetuity is an annuity that continues forever. The capital value of a perpetuity is the present value of all (future) payments. (Perpetuities are also called permanent endowments, and the continuous case was treated on pages 408 – 409 using improper integrals.) 

    

The capital value of a perpetuity that pays $1000 annually, beginning now, at an interest rate of 8% compounded annually is

  

     

 Find this value.

1000 + 1000 1 + 0.08 + 1000 (1+0.08) + 1000 (1+0.08)