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Matthias Doepke - Marcroeconomics - Chapter 1

Chapter 1 Preliminaries This chapter introduces interest rates and growth rates. The two topics are closely related, so we treat them together. The concepts discussed here are not in Barro, but they will help you understand the graphs and statistics that he uses throughout his book. | Chapter 1 Preliminaries This chapter introduces interest rates and growth rates. The two topics are closely related so we treat them together. The concepts discussed here are not in Barro but they will help you understand the graphs and statistics that he uses throughout his book. 1.1 Compound Interest We begin with some common terms and calculations from the realm of fixed-income investments. The amount of the investment is called the principal. The fixed-income from the investments is called interest. The interest per unit of principal per unit of time is called the interest rate. Most commonly interest rates are quoted in dollars per year per dollar of principal. These units can be written y . The dollar units cancel so this interest rate has units of one over years. Similarly if the interest rate is apples per day per apple borrowed the apple units will cancel and the units of the interest rate will be one over days. In general the units of an interest rate are one over some unit of time. When the unit of time is a year we say that an interest rate is an annual interest rate. If the unit of time is not mentioned then it will almost always be an annual interest rate. Interest rates that are quoted in some specific unit of time can be converted to any other unit of time via a simple linear transformation. For example a daily interest rate of x corresponds to an annual interest rate of 365 x .1 See Exercise 1.1 for an example. We use P for the principal of a fixed-income investment and P for the annual interest rate. Under simple interest the interest is earned on the amount of the principal only. In this case 1You may be wondering about leap years. These are handled according to any of a number of conventions. For example some interest rates are quoted using 360 days as a year others use 365 still others use 365.25. 2 Preliminaries after n years the value of the investment will be 1.1 Vs n RPn P. For example suppose you invest 5 000 at a 4.5 simple annual .