Question

John Wong makes $63,800 per year maintaining a self-storage business.

He was notified of a 3.3% raise in a year in which the CPI index increased
by 4.4%.

Find the gain or loss in his purchasing power.


loss of $701.80

gain of $701.80

loss of $2105.40

gain of $2105.40

Answer 1

To find the purchasing power you work in two stages:

1) calculate the new income using the percent raising. In this case 3.3%.

2) deflate the new income with the inflation rate. 4.4% in this case.

So, let's work:

1) New income

new income = old income + raise

raise = old income × raising rate = 63,800 × 3.3/100 = 2.105.4

new income = 63,800 + 2,105.4 = 65.905,4

2) Deflate the new income

CPI increase by 4.4% ⇒

price index of previous year = 100
price index of new year = 104.4

⇒

  100            x
--------- = ------------
104.4      65,905.4

⇒ x = 65,905.4 × 100 / 104.4 = 63,127.7

So, the change on the purchasing power is the difference 63,127.7 - 63,800 = - 672.3

And the negative sing means a loss.

The closest answer from the answer choices is loss of $ 701.80