Suppose the Social Security Administration would like to guarantee the purchasing power of social security payments to the elderly does not diminish
That is, the real value of the payments does not decrease. The CPI in 1990 was 130.7 and the CPI in 1998 was 163.0. How much does the Social Security Administration need to increase payments from 1990 to 1998 to accomplish this objective?
The change in the general price level is 100(163-130.7)/130.7 = 25%. Thus, the level of payments in 1998 need to be P(1990)*(1+0.25).
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