Quiz 4 Examples - Quiz 4 Examples 1. Suppose the ratio of...

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Quiz 4 Examples 1. Suppose the ratio of China’s GDP to U.S. GDP is rising 4% a year. How long will it take to double? Use the “rule of 70,” or rt=0.70, where r is a rate of growth and t is the number of years required to double. Then r = 4% = 0.04 and t = 0.70/0.04 = 18.5 years. The rule of 70 is an approximation from Xt/X0 = e rt , and e 0.693 = 2. The text uses a looser approximation, the “rule of 72,” from banking. It’s easier to apply to monthly data, since 72 is divisible by 12. 2. Suppose the nominal debt grows 6% a year and nominal GDP grows 2% a year. How long will it take the ratio of the debt to GDP to double? Let z = x/y. Then for low rates of growth, z* = x* - y* is an okay approximation, where * indicates rate of growth. Let ratio = debt/GDP. Then ratio* = debt* - GDP* = 6% - 2% = 4%. If something is growing at 4% a year, it will double in 18.5 years, by the rule of 70. 3. If India’s GDP quadruples in 24 years, what is its rate of growth? To quadruple, something had to double two times.
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Quiz 4 Examples - Quiz 4 Examples 1. Suppose the ratio of...

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