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06 010 4year similarly if your nominal income grows

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= 0.06 – 0.10 = –4%/year. Similarly, if your nominal income grows at an instanta- neously compounded annual growth rate of 8%/year and all prices are rising at 3%/year, then your real income is growing at a rate of exactly 0.08 – 0.03 = 5%/year. And so on. Economists use such exponential functions not to make their work harder, but to make it easier! 2. Exercises 1. Left-handed Louie, your friendly neighbourhood loan shark, has agreed to advance you $1000. You can choose (a) his regular interest rate of 2%/day on the outstand- ing balance (calculated daily), or (b) his special interest rate of 10%/week on the out- standing balance (calculated weekly). If you are unable to pay for 52 weeks (364 days), and Louie simply adds your interest to the outstanding balance, then how much do you owe him at the end of this time, under each of the plans? 2. In 2010, Unidyne Enterprises’ annual sales hit $100,000,000, and they are projected to grow at a rate of 25%/year for the foreseeable future. When do you expect Unidyne’s sales to reach $300,000,000 per year? 3. Between 2010 and 2011, the Consumer Price Index rose from 250 to 275 in Leutonia, while in Granfaloonia, it rose over the same period from 88 to 97. In which country is the rate of inflation higher? 4. Calculate the present discounted value of $100 paid exactly 5 years from today, when the interest rate i is: (a) 0%/year; (b) 5%/year; (c) 10%/year; (d) 20%/year; (e) 50%/year; (f) 100%/year. Then repeat your calculations if the $100 is paid exactly 10 years from today. 5. Suppose that your nominal income grows at a constant, instantaneously com- pounded rate of 5%/year, while the Consumer Price Index (CPI) grows at a con- stant, instantaneously compounded rate of 3%/year. In 2010, your nominal income is $100,000. How fast is your income rising in real terms? In terms of 2010 dollars of constant purchasing power, what will your real income be in 2015? 6. You are offered an opportunity to receive three payments: $8000 one year from today, another $8000 two years from today, and a third $8000 three years from today. If these payments are guaranteed and risk-free, what is the most you should pay for the opportunity if the rate of interest is 5%/year? if the rate of interest is 15%/year? MATH MODULE 9: GROWTH RATES, INTEREST RATES, AND IN±LATION: THE ECONOMICS O± TIME M9-7
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7. In 2010, the country of Exponentia (where all variables grow at a constant, instanta- neously compounded rate) has a Gross Domestic product of 200,000 zlotniks/year and a population of 800 people. Its nominal GDP grows at 10%/year, its rate of infla- tion is 5%/year, and its population grows at 2%/year. What is its GDP per capita in 2010, and (in 2010 zlotniks of constant purchasing power) in what year will its real GDP per capita reach 500 zlotniks per person? 8. The price of Wedgios men’s fashion boxer shorts rose from $12/pair to $13/pair between 2010 and 2013, while over the same period, the Consumer Price Index rose from 80 to 96. What was the average annual rate of increase in the price of Wedgios relative to other consumer goods over the period? M9-8 MATH MODULE 9: GROWTH RATES, INTEREST RATES, AND INFLATION: THE ECONOMICS OF TIME
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06 010 4year Similarly if your nominal income grows at an...

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