A family friend is retiring from work in the U. S. She is exactly 62 years old right now (time 0) and has the choice of taking her Social Security (a public pension program) right now or delaying according to the following schedule:

I. Early retirement (Age 62 exactly)
11. Regular retirement (Age 66 years, 2 months)
III. Delayed retirement (Age 70 exactly) $800 per month for life $1,000 per month for life $1,240 per month for life If her expected life expectancy is 80 years old (exactly), what are the present values of the choices? (Assume r-6% (annual))

Manipulation manufacturing's (amm) standards anticipate that there will be 5 pounds of raw material used for every unit of finished goods produced. amm began the month of maymay with 8,000 pounds of raw material, purchased 25,500 pounds for $ 15,300 and ended the month with 7,400 pounds on hand. the company produced 4,9004,900 units of finished goods. the company estimates standard costs at $ 1.10 per pound. the materials price and efficiency variances for the month of maymay were:

1. revising for conciseness - eliminating flabby expressions,limiting long lead-ins, and dropping unnecessary fillerstime is money in any business environment. people want information communicated quickly and clearly. to make your writing more concise and understandable, avoid flabby expressions, long lead-ins, and unnecessary fillers. your audience will appreciate your brevity.1. if your writing contains a flabby expression like in view of the fact that, replace it with the word because / although / probably .for each of the following two sentences, choose the best revision.2. i am sending you this letter to inform you that we have experienced an unexpected surprise within our expense sheet, but we are positively certain we will solve it.1) we need to inform you that we have experienced an unexpected surprise with our expense sheet, but we are midway to an end result.2) we have identified a problem with our expense sheet, but we will solve it.3) i am sending you this letter to inform you that we have a problem with our expense sheet, but we are positively certain we have a solution.3. it is the user who should contact the center.1) everyone knows that it is the user who should contact the center.2) the user should contact the center.3) if there is a problem, the user should contact the center.read the following passage, and then answer the question.[1] you scheduled seven conference calls for this morning between 10 and 11 a.m. [2] generally, the company limits the number of conference calls to three per hour. [3] i’m letting you know that in the future, we should be more careful about scheduling.4. which revision limits the long lead-in in sentence 3? 1) in the future, we should be more careful about scheduling.2) i’m letting you know so that in the future we are more careful about scheduling calls.3) so that you know in the future, we should be more careful about scheduling.

China's new 5 percent tax on disposable wooden chopsticks, reflecting concerns about deforestation, has been praised by environmentalists. the move is hitting hard at the japanese, who consume 25 billion set of wooden chopsticks annually. almost all of the chopsticks used in japan come from china. the reuirements for chinese manufacturers of wooden chopsticks to pay the 5 percent tax is a factor in their external environment.