Aaron’s plan is to put $100 at the beginning of each month into a savings account which pays 4.5% interest, compounded monthly. As usual, interest is paid at the end of each month on money which has been in the account all month; in other words, the first deposit does earn interest during the first month. If he starts saving $100 per month when he is 25, how much will he have in the account when he turns 70? [Assume that he makes 12 deposits when he is 25, another 12 when he is 26, etc., but no more deposits once he is 70.]

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.