A family wishes to accumulate 50,000 i a college education fund by the end of 20 years. If they deposit 1,000 into the fund at the end of each of the first 10 years, and 1, 000+X at the end of each of the second 10 years, find X to the nearest unit if the fund earns 7% effective.

Anew 2-lane road is needed in a part of town that is growing. at some point the road will need 4 lanes to handle the anticipated traffic. if the city's optimistic estimate of growth is used, the expansion will be needed in 4 years and has a probability of happening of 40%. for the most likely and pessimistic estimates, the expansion will be needed in 8 and 15 years respectively. the probability of the pessimistic estimate happening is 20%. the expansion will cost $ 4.2 million and the interest rate is 8%. what is the expected pw the expansion will cost?

The third program provides families with $50 in food stamps each week, redeemable for both perishable and nonperishable food. the fourth policy instead provides a family with a box of nonperishable foods each week, worth $50. use two graphs to illustrate that a family may be indifferent between the two programs, but will never prefer the $50 box of nonperishable foods over the $50 in food stamps. state your answer and use a consumer choice model for perishable food and nonperishable food to graphically justify your choice.

Wyome has a career in manufacturing and goes to an office to work every day. at the office, he most likely works with