This Problem Demonstrates the Dependence of the Present Value of an Annuity

Essay

This problem demonstrates the dependence of the present value of an annuity on the number of payments. Using 7% compounded annually as the discount rate, calculate the present value of an ordinary annuity paying $1,000 per year for:
a) 5 years b) 10 years c) 20 years d) 30 years e) 100 years f) 1,000 years
Observe that the present value increases with increasing n, but at a diminishing rate. In this case, the 970 payments from Year 30 to Year 1,000 cause the present value to increase by only about 15%.