In the text we said that, over many years, small differences in growth rates can have large effects on the level of income. This question will help you understand this important point. Consider an initial value of real GDP equal to \(Y_{0}\). If real GDP grows at a rate of \(g\) percent annually, after \(N\) years real GDP will equal \(Y_{0}(1+\) \(g)^{N}\). Now consider the following table. Let the initial level of GDP in all cases be 100 .

a. By using the formula provided above, compute the level of real GDP in column 1 for each year. For example, in Year 1 , real GDP will equal 100 (1.01) \({ }^{1}\) \(=101\). For each year, compute the GDP to two decimal places.

b. Now do the same for the rest of the columns.

c. In Year 20 , how much larger (in percentage terms) is real GDP in the 3 percent growth case compared with the 1 .5 percent growth case?

d. In Year 50 , how much larger (in percentage terms) is real GDP in the 3 percent growth case compared with the 1 .5 percent growth case?

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Real GDP with Alternative Growth Rates: 1% 1.5% 2% 2.5% 3% 3.5% Year (1) (2) (3) (4) (5) (6) 0 100 100 100 100 100 100 1 3 5 10 20 30 50