Assignment

1. Greg borrows $2,500 for 4 years at 7% simple interest (annual rate). How much interest will be paid in dollars?
A.) $250 B.) $400 C.) $600 D.) $700

2. The Schwartz Bank wants to earn 8.2% simple discount interest on a 90 day $1.5 million Treasury bill. How much should the bank pay? The bank uses 360 days per year when computing daily interest.
A.) $1,632,045 B.) $1,469,250 C.) $1,437,250 D.) $1,390,360

3. Cindy deposits $20,000 into an 8% CD compounded annually for 5 years. How much money is in her CD account at the end of the 5 years?
A.) $29,386.56 B.) $28,943.87 C.) $29,934.95 D.) $28,389.65

4. Jan deposits $20,000 into an 8% CD compounded quarterly for 5 years. How much money is in her CD account at the end of the 5 years?
A.) $29,329.38 B.) $28,997.40 C.) $29,718.95 D.) $29,581.93 5. Approximately how long would it take for your investment to double if you invested at 7% compounded annually?
A.) 10.24 years B.) 10.82 years C.) 11.05 years D.) 11.87 years

6. Bobby's retirement plan includes an account in which he invests $100 a month at a rate of 7.6% compounded monthly. Bobby continues to make payments into this account for 40 years at which time he will be 65 years old. How much money will he have in this retirement account when he retires at age 65? (Note: payments are made at the end of each period, and use i = .076/12 = 0.00633 rounded to the fifth decimal place).
A.) $234,087.49 B.) $245,820.51 C.) $278,362.95 D.) $310,788.37

7. Marsha is planning to buy a $10,000 used car after graduation. She will graduate in 4 years. How much money will she need to save quarterly if he invests in an account paying 8% compounded quarterly. (Assume she invests for the complete four years.)
A.) $536.50 B.) $549.32 C.) $570.32 D.) $521.59

8. You are given the following two scenarios: Scenario X: Alice invests $100 at 10% simple annual interest for 3 years Scenario Y: Alice invests $100 at 10% compound annual interest for 3 years. Which one of the following statements is correct? (Hint, graphing may help at time intervals of ½)
A.) At all points in time, scenario X earns more than scenario Y. B.) At all points in time, scenario Y earns more than scenario X. C.) Between the times of 0 and 1 (exclusive of 0 and 1), scenario X earns more than scenario Y. At the time of 1, scenario X earns the same as scenario Y. Between the times of 1 and 3 (exclusive of 1), scenario Y earns more than scenario X. D.) Between the times of 0 and 1 (exclusive of 0 and 1), scenario Y earns more than scenario X. At the time of 1, scenario X earns the same as scenario Y. Between the times of 1 and 3 (exclusive of 1), scenario X earns more than scenario Y.

9. Peter borrows $15,000 from the Schwartz Bank to purchase a car. The interest rate is 6.5% compounded monthly with payments due every month. If the loan is amortized over 4 years, how much are the monthly payments?
A.) $340.87 B.) $346.29 C.) $350.73 D.) $355.75

10. Mike and Carol borrowed $60,000 to buy their house (30 year mortgage). The monthly payments are $617.17 and the interest rate is 1% per month. What is the balance of their mortgage after 15 years?
A.) $51,422.09 B.) $32,546.05 C.) $33,106.56 D.) $34,398.28

11. Let P be the statement "Tiger is a dog", and let Q be the statement "Fluffy is a cat". Then which of the following statements represent (~P Λ ~Q).
A.) Tiger is not a dog, and Fluffy is a cat. B.) Tiger is not a dog, and Fluffy is not a cat. C.) Tiger is a cat, and Fluffy is a dog. D.) Tiger is not a cat, and Fluffy is not a dog.

12. Let P be the statement "Sam will work at the butcher shop tonight", and Q be the statement "Sam will go bowling tonight". Then which of the following statements represent [~ (P V Q)]. Be careful on this one.
A.) Sam will work at the butcher shop tonight and Sam will go bowling. B.) Sam will not work at the butcher shop tonight or Sam will not go bowling. C.) Sam can't work tonight or bowl tonight because he has a date with Alice. D.) Sam will not work at the butcher shop tonight and Sam will not go bowling tonight.

13. Is the following truth table correct or incorrect? P Q P V ~Q (P V ~Q) Λ Q
P= T T FF Q=T F T F P V ~Q=T T F T (P V ~Q) Λ Q= T F F F
A.) Correct B.) Not Correct

14. è Q) Λ (Q èAre the following two statements logically equivalent? (P R)
A.) Yes, they are logically equivalent. B.) No, they areèR), and (P not logically equivalent.

15. Are the following two statements logically equivalent? p V (q Λ r), and (p V q) Λ (p V r)
A.) Yes, they are logically equivalent.
B.) No, they are not logically equivalent.