You started planning for your retirement. Assume a fixed horizon (given below) and a given annual inflation rate. For the first years you will be making contributions at the beginning of the year (adjusted for the inflation beginning in year 2) in order to meet the following retirement goal: Starting in year K, withdraw a desired amount (IN TODAY'S DOLLARS) at the beginning of each year until the end of the horizon. For the first few years, you will be using more aggressive investments (higher expected return). For the next few years assume a different return another for the remainder of the years. Build a model to answer the question: What is the minimum first contribution to accomplish such a retirement goal

The business cycle is the periodic but irregular up-and-down movement in economic activity, measured by fluctuations in real gross domestic product (gdp) and other macroeconomic variables. a business cycle is typically characterized by four phases—recession, recovery, growth, and decline—that repeat themselves over time. economists note, however, that complete business cycles vary in length. the duration of business cycles can be anywhere from about two to twelve years, with most cycles averaging six years in length. some business analysts use the business cycle model and terminology to study and explain fluctuations in business inventory and other individual elements of corporate operations. but the term "business cycle" is still primarily associated with larger (industry-wide, regional, national, or even international) business trends.

Answer analog;