Question

Social Security recipients receive an automatic cost-of-living adjustment (COLA) once each year. Their monthly benefit is increased by the amount that consumer prices increased during the preceding year. Suppose that consumer prices have increased by 5.4% during the preceding year.

(a) Express the adjusted monthly benefit of a Social Security recipient as a function of his or her current monthly benefit.
I(x) =

(b) If Harrington's monthly Social Security benefit is now $520, what will be his adjusted monthly benefit?
$

Answer 1

The adjusted monthly benefit of a Social Security recipient can be calculated using the formula I(x) = (1 + COLA) * x. If Harrington's current monthly benefit is $520 and the consumer prices increased by 5.4%, his adjusted monthly benefit would be $547.68.

Step-by-step explanation:

(a) The adjusted monthly benefit of a Social Security recipient as a function of his or her current monthly benefit, can be expressed by:

I(x) = (1 + COLA) * x

Where x is the current monthly benefit and COLA is the cost-of-living adjustment as a decimal.

(b) If Harrington's current monthly Social Security benefit is $520 and the consumer prices have increased by 5.4%, his adjusted monthly benefit can be calculated as follows:

I(x) = (1 + 0.054) * 520

I(x) = $547.68

Answer 2

Part A:

Social Security recipients receive an automatic cost-of-living adjustment (COLA) once each year.

Lets say that the benefit for the previous year was p, and a COLA of 5.4% is added, the new benefit will be :

`p+0.054p=1.054p`

Part B:

Harrington's adjusted monthly benefit will be =
`1.054(520)=548.08` dollars.