A government provides each citizen over the age of 65 with a monthly pension payable for life. The current monthly payment is 400. The payment is indexed to inflation so that every year there is an adjustment to reflect the rate of inflation for the year (but payments within a year are level). The government proposes a cost-cutting measure whereby the payments will be "partially de-indexed", so that the payment increase will be the excess of the inflation rate over 3%. The increase is 0 if the inflation is less than 3%. As a simplified model the government regards the lifetime payments as a perpetuity. What are the pension present values both before and after de-indexing under each of the following annual interest/inflation scenarios.

(a) i = 0.12, r = 0.09

(b) i = 0.12, r = 0.03

(c) i = 0.09, r = 0.06

(d) i = 0.06, r = 0.03

(Answer: (a) PV before de-indexing is 168,620, after de-indexing it is 84,310, (b) PV before de-indexing is 56,207, after de-indexing it is 42,155, (c) PV before de-indexing is 166,497, after de-indexing it is 83,249, (d) PV before de-indexing is 164,354, after de-indexing it is 82,177)