# Mathematics

Directions: This is a take home test. It is due at the beginning of the next class after it is issued. You are allowed to use your textbook, corrected papers for this course, and your notes. You may also use a graphing calculator. You may not use any computer, smartphone, internet site, or any other similar electronic aid. When you put your name on this test you verify that you understand and comply with the rules of this test.

You may work on this test with any member(s) of this class. You may not discuss it with any other person outside of the class. You may discuss questions with RPH.

Do all problems in order on 8.5 x 11 inch paper or graph paper. **WRITE ON ONLY ONE SIDE OF EACH PAGE TO HELP IN THE CORRECTION AND GRADING.** Problems must be done in the numerical order given. **Staple your pages in order with this test question sheet on top.** Show all work. Answers without corresponding work may not be graded correct or awarded any partial credit. Present your work neatly, in an organized manner, with detail.

This examination is due at the beginning of class on March 1, 2018. Late papers will not be accepted.

Electronic submissions will not be accepted.

Each of the major questions is worth an equal amount. Your grade will be calculated on a percentage basis (from 0% to 100%). Partial credit may be given.

1.) Calculate the simple interest for an investment with an initial principal of $10,500, an interest

rate of 4.85% per year, and the time period of 3 years and 3 months. Show your work and

answer.

2.) Calculate the compound interest for an investment with an initial principal of $10,500, an

interest rate of 4.85% per year, and a time period of 3 years 3 months. Compounding should

be done monthly. Show your work and answer.

3.) Stephanie Garcia must pay a lump sum of $10,500 in 5 years. What amount

deposited today at 3.8% interest compounded annually will amount to $10,500 in 5 years?

(Hint: Use the present value for compound interest formula.) Show your work and correct

answer.

4.) What amount would need to be invested weekly (52 weeks per year) to have an investment

worth $1,500,000 in 30 years if the interest rate was 7.5%? Assume that the first investment

would be made at the time that the investment plan was initiated (making this an annuity due).

5.) The Anderson family buys a house for $325,000 with a down payment of $85,000. The family

takes out a 30 year amortized mortgage on the remaining cost of the home at an annual interest

rate of 3.6%. Payments (principal and interest) of equal amount are paid monthly. Find the

amount of the monthly payment needed to amortize this loan. Show your work and correct

answer.

6.) Consider the Anderson family’s purchase of a house described in problem #5. At the end of

12 years the Andersons inherit some money and want to pay the remaining balance on the

amortized loan. What would the this remaining balance?

7.) You win a lottery prize that has a total value (after taxes) of $35,850,000. 30 yearly payments of

$1,195,000 would be made if you took the winnings over the 30 year payout with the first

payment being made immediately and the remaining equal payments being made yearly at the

beginning of each year. The lottery would buy an annuity which has an annual interest rate of

5.2%. You elect the alternative and take the cash value of this annuity now. You calculate that

you can make more money by investing the winnings at a higher rate than 5.2%. What is the

cash value of this annuity?

8.) You graduate from college and start work. You set up an investment plan whereby you

contribute $125 from each of your monthly paychecks and get 5.4% interest compounded

monthly. You have your first payment payroll deducted and deposited into the IRA (individual

retirement account) at the end of your first month’s work. If you intend to work for

45 years, what will be the value of this investment when you retire?

9.) You are buying a car that cost $26,500. You make payments of $412 each month for 4 years.

The interest rate charged on the amount owed after you made the down payment is 2.9%

per year. What will be the amount of your down payment?

10.) When you save money in a bank savings account the interest is calculated continually. This

involves using a formula with e. Assume that the annual interest rate is 3%. If you make a

one- time deposit of $6,800 into this type of bank savings account,

a.) What will be the total value in the account at the end of 5 years and 9 months?

(3/4 credit)

b.) What will be the amount of the interest earned at the end of 5 years and 9 months?

(1/4 credit)

11.) You have steady employment and earn a regular salary. You have saved $5400 that you want

to invest in a certificate of deposit that pays a stated rate (nominal rate) of 4.6%. The interest

on this CD is compounded weekly (52 weeks in a year for banking purposes). What is effective

rate (annual percentage rate, APY)? (Hint: The effect rate should be greater than the nominal

rate.)

12.) Consider the future value of an ordinary annuity and an annuity due.

a.) Explain the difference between these two types of annuities.

b.) Which of these plans will produce a greater value at the end of the total time period for the

annuity? Why is this so?

(Answer thoroughly using complete sentences.)

13.) Solve the following linear system using your graphing calculator and matrix commands. Give

your answers and describe the process you used (the calculator steps) to find the solution.

Hint: There is a definite solution to this system. It is not unsolvable.

x – y + 5z = -6

3x + 3y – z = 10

x + 2y + 3z = 5

14.) Solve the linear system shown in #13 above using the Gauss-Jordan method. Show all steps

one under another on the left in a single column and to the right show any needed calculations

and give the correct corresponding transition commands (Example: R1 <— R1 + .5 R2). Detail

is needed for credit. Work until you reach the row echelon format and back solve.

To get you started:

Show original system of 3 equations here.

1st transition (Show complete new system.) work for 1st transition and transition

command (as in the example shown

above)

2nd transition work for 2nd transition

etc.

(Show the remaining steps too.)

Back solving work and answers here