MATH 106 NAME: ___________________________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 7 problems, some with multiple parts. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You have to submit your answer document in your Assignments Folder in a readable format (.doc or .PDF format) no later than 11:59 pm on Sunday, Sept 3. Show work/explanation where indicated. Answers without any work may earn little or no credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work (in jpg or pdf format is acceptable also. In your document, be sure to include your name and the assertion of independence of work. If you have any questions, please contact me by e-mail (pkudva@faculty.umuc.edu).. 1. (28 points) To purchase a house, a homebuyer takes out a mortgage, borrowing $290,000 at the annual interest rate 4.2%, compounded monthly for 30 years. (The problem has four parts.) (a) Calculate the monthly payment. Show how to carry out the calculation. (b) Calculate the total interest paid if the loan is held for the entire term. Show some work. 1 MATH 106 (c) Complete the following table. (Round amounts to the nearest cent.) Payment number Interest Paid Principal Paid Unpaid balance 1 2 Show the calculations necessary to arrive at the entries in the table. (d) Calculate the unpaid balance after 6 years. What percentage of the amount borrowed is still unpaid? Show work. 2 MATH 106 2. (16 points) Albert makes a one-time deposit of $9,000 in a savings account at 6.9% annual interest compounded monthly. Betty deposits $150 into a savings account at the end of every month for 7 years at 6.9% annual interest compounded monthly. (a) How much will Albert have in his account at the end of seven years? Show work. (b) How much will Betty have in her account at the end of seven years? Show work. (c) Who has more money in his/her account at the end of seven years and by how much, Albert or Betty? (d) How much has each person earned in total interest, at the end of seven years? Who earned more in total interest and by how much? Show work. 3. (10 points) 3 MATH 106 Parents have set up a sinking fund in order to have $160,000 in 16 years for their children's college education. How much should be paid quarterly into an account paying 4.8% compounded quarterly? Round answer to the nearest cent. Show work. 4. (6 points) If a bank pays 2.4% interest compounded monthly on its certificates of deposit (CDs), what is the effective interest rate? Give answer as a percentage; round answer to nearest onehundredth of a percent. Show work. 5. (15 points) You have $20,000 to invest in a retirement savings account. Financial Investments offers a retirement account with 4.57% interest compounded monthly, while Safe Associates offers a 4 MATH 106 retirement account with 4.6% interest compounded semi-annually. If you are thinking of investing this money for 6 years, which account gives you a better return? Why? (show work) 6. (10 points) What is the present value of an ordinary annuity that pays $1200 quarterly for 5 years at 6.4% compounded quarterly? Round answer to the nearest cent. Show work 7. (15 points) An industrial firm needs a $40,000 piece of machinery that has a useful life of 5 years. Knowing that the machine will have to be replaced every 5 years, the firm has the option of leasing a machine for $10,000 per year, or borrowing $40,000 to buy the machine. The 1 st National Bank can provide a $40,000 loan at 7.8% compounded annually over 5 years. Over 5 MATH 106 the 5-year life of the machine: is it cheaper to lease, or to borrow the money and buy the machine? Show all work to support your choice: a simple \"one or the other\" answer, even if it's correct, will result in zero credit! 6