3. Suppose you have built up a pension with $12,000 annual payments by working 10 years for a company when you leave to accept a better job. The company gives you the option of collecting half the full pension when you reach age 55 or the full pension at age 65. Assume an interest rate of 8% compounded annually. (5 pts. 3 and 2 pts. respectively)

a) By age 75, how much will each plan produce?

b) Which plan would produce the larger amount?

4. The Fix family bought a house for $210,000. They paid $42,000 down and took out a 30-year mortgage for the balance at 3.75%. (8 pts. each question 2 pts.)

a) Find the monthly payment.

b) How much of the first payment is interest?

After 15 years, the family sold their house for $255,000.

c) Estimate the current mortgage balance at the time of sale.

d) Find the amount of money they receive from the sale after paying off the mortgage.

5.

Part I.

Find the APY corresponding to the given nominal rate. (7 pts Part I 3 pts, Part II 2 pts, Part III 2 pts)

a) 6.5% compunded daily b) 6.5% compounded monthly c) 6.5% compounded quarterly

Part II

What do you notice about the APY as the frequency of compounding decreases?

Part III

In your own words describe the importance of APY for customers.

6. A store sells televisions for $400 and DVD players for $150. At the beginning of the week its entire stock is worth $60,000. During the week it sells three quarters of the televisions and one third of DVD players for a total of $ 40,000. How many televisions and DVD players did it have in its stock at the beginning of the week? (3 pts.)

7. Let ]. (2 pts.)

Find 3U+4V.

8. A simplified economy is based on the agriculture, manufacturing, and transportation. Each unit of agriculture output requires 0.4 units of its own output, 0.3 unit of manufacturing output, and 0.2 unit of transportation output. One unit of manufacturing output requires 0.4 unit of its own output, 0.2 unit of agricultural output, and 0.3 unit of transportation output. One unit of transportation output requires 0.4 unit of its own output, 0.1 unit of agricultural output, and 0.2 unit of manufacturing output. There is demand for 35 units of agricultural, 90 units of manufacturing, and 20 units of transportation output. How many units should each segment of the economy produce? (4 pts.)

9. Find the inverse, if it exists, of the given matrix. (3 pts.)

Show work below.

10. The activities of a grazing animal can be classified roughly into three categories: grazing, moving, and resting. Suppose horses spend 8 hours grazing, 8 moving, and 8 resting; cattle spend 10 grazing, 5 moving, and 9 resting; sheep spend 7 grazing, 10 moving, and 7 resting; goats spend 8 grazing, 9 moving, and 7 resting. Write this information as 4x3 matrix. Label rows and columns appropriately. (2 pts.)