Question

4) In 1991, the Barenaked Ladies released their hit song “if I had a Million Dollars.” How much money would the group need in 2017 to have the same amount of real purchasing power that they did in 1991? Note that the consumer price index in 1991 was 136.2 and in 2017 it was 244. Show your work for credit .

5) While rooting through the attic you discover a box of old tax forms. You find that your grandmother made $75 working part-time during December 1964 when the CPI was 31.3. How much would you need to have earned in in July of 2018 to have at least as much real income as your grandmother did in 1964? The CPI for July 2018 was 252.006. Show your work for credit.

Answer 1

Part 1) We have the following information

Consumer Price Index (CPI) in 1991 = 136.2

Consumer Price Index (CPI) in 2017 = 244

Taking 1991 as the base year and 2017 as the target year

First, we will calculate the change in the purchasing power during the period of 1991 to 2017 by using the following formula

(CPI of Base Year/CPI of Target Year) × 100 = (136.2/244) × 100 = 55.82%. It means that during the period of 1991 to 2017 the purchasing power of a single dollar has declined by 100% – 55.82% = 44.18%.

Now we will do the equivalent dollar calculation using the following formula

(CPI of Target Year/CPI of Base Year) × 1 Million Dollars

(244/136.2) × 1,000,000

$1,791,483.11

So, the group would need $1,791,483.11 in 2017 to have the same real purchasing power that they did in 1991.

Part 2) We have the following information

Consumer Price Index (CPI) in December 1964 = 31.3

Consumer Price Index (CPI) in July 2018 = 252.006

Taking December 1964 as the base and July 2018 as the target

First, we will calculate the change in the purchasing power during the period of December 1964 to July 2018 by using the following formula

(CPI of Base /CPI of Target) × 100 = (31.3/252.006) × 100 = 12.42%. It means that during the period of December 1964 to July 2018 the purchasing power of a single dollar has declined by 100% – 12.42% = 87.58%.

Now we will do the equivalent dollar calculation using the following formula

(CPI of Target/CPI of Base) × 75

(252.006/31.3) × 75

$603.85

So, one would need $603.85 in July 2018 to have the same real income that one’s grandmother had in December 1964.