The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.6 trillion?

Question

Mathematics

Mattie Cruz

20 May, 21:31

The annual Gross Domestic Product (GDP) of a country is the value of all of the goods and services produced in the country during a year. During the period 1985-1999, the Gross Domestic Product of the United States grew about 3.2% per year, measured in 1996 dollars. In 1985, the GDP was $577 billion. I what year did/or will the GDP equal $1.6 trillion?

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Answers (1)

Know the Answer?

Tristen Hooper · Answer 1

Given:

GDP = $577 billion = $0.577 trillion in 1985.

Annual growth rate = 3.2% = 0.032

After 1 year, the GDP will be $ 0.577 (1.032) trillion

After 2 years, the GDP will be $ 0.577 (1.032) ² trillion

...

After n years, the GDP will be $ 0.577 (1.032) ⁿ trillion.

The number of years required from 1985 for the GDP to reach $ 1.6 trillion is

determined by

0.577 (1.032) ⁿ = 1.6

1.032ⁿ = 1.6/0.577 = 2.773

n ln (1.032) = ln (2.773)

n = ln (2.773) / ln (1.032) = 32.4 years

From 1985, the year is

1985 + 32.4 = 2017.4

Answer:

The GDP will reach $1.6 trillion in the year 2017 if the average growth rate of 3.2% is maintained.