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In 1980, when the consumer price index (CPI) was 82.4, Ivan purchased a house for $71,900. Assuming that the price of houses increased at the same rate as the CPI from 1970 to 1980, approximately how much would the house have cost in 1970, when the CPI was 38.8?

Respuesta :

x = (71,900)(38.8/32.4)= 33855.8252427184466= $33,900

Answer:

$33,856

Step-by-step explanation:

We have been given that in 1980, when the consumer price index (CPI) was 82.4, Ivan purchased a house for $71,900. The CPI in 1970 was 38.8. We are asked to find the cost of house in 1970.

[tex]\text{Past dollars in terms of recent dollars}=\text{Dollar amount}\times \text{Ending-period CPI}\div\text{ Beginning-period CPI}[/tex]

Substitute the given values:

[tex]\text{Cost of house in 1970}=\$71,900\times 38.8\div 82.4[/tex]

[tex]\text{Cost of house in 1970}=\$71,900\times 0.470873786407767[/tex]

[tex]\text{Cost of house in 1970}=\$33,855.825242718[/tex]

[tex]\text{Cost of house in 1970}\approx \$33,856[/tex]

Therefore, the cost of house in 1970 was $33,856.

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