Download MATH 1090-2 Practice Final: Sequences, Loans, Quadratics, Functions and more Exams Mathematics in PDF only on Docsity! MATH 1090-2: PRACTICE FINAL 1 December, 2007 1. True or False: (a) Every sequence of real numbers is either arithmetic or geometric. (b) If a1, a2, . . . is a geometric sequence, then a1/a2 = a3/a4. (c) One dollar invested for one year at a 6% annual interest compounded continuously will be worth more than one dollar invested at a 6% annual rate compounded quarterly. (d) The sequence 1, 2, 4, 8, . . . is arithmetic. (e) If A and B are square matrices then their product AB exists. (f) The graph of a quadratic equation always crosses the x-axis in two points. (g) ln(a + b) = ln(a) + ln(b). (h) (x + 1)2 = x2 + 1. (i) The domain of f(x) = √ x consists of all real numbers. (j) Taking 1090 was a life-enhancing experience. 2. Suppose you have your heart set on a $15, 000 car. If the interest rate on the loan is 12% (annually) compounded monthly, and you want to make monthly payments of $400 for three years, how much must you have for a down payment? 2*. Your parents are renovating their kitchen and they consult you for some mathematical advice. They plan on purchasing $20, 000 worth of material for the renovation by making a $3, 000 down payment and amortizing the rest with quarterly payments over the next five years. The 12% annual interest rate on the loan is compounded quarterly. Find (a) the size of their quarterly payments; (b) the total amount paid over the life of the loan; and (c) the total interest paid over the life of the loan. 2**. You wish to retire at age 65 and draw $4, 000 at the end of each month for the net 25 years. If your money is invested in an account earning 9% annually which is compounded monthly, how much must you have in the bank at age 65? 1There are more problems on this practice final than on the actual final exam. To get a feel for the length of the actual exam, you should choose one problem numbered 1, one problem numbered 2, and so on. 3. Find the sum of the first thirty terms of the geometric sequence 1, 0.99, (0.99)2, (0.99)3, . . . . 3*. Find the sum of the first 100 terms of the arithmetic sequence 2, 5, 8, 11, 14, . . . . 4. How much is one dollar worth one year after investing it in an account earning 10% annually compounded monthly? 4*. How much is one dollar worth one year after investing it in an account earning 12% annually compounded continuously? 5. Compute the interest for: (a) an initial investment of $1000 earning a simple annual interest rate of 12% for 10 years; (b) an initial investment of $1000 earning an annual interest rate of 8% compounded quarterly for 10 years. 6. Determine if the following sequences are arithmetic, geometric, or neither: (a) 1, 2, 3, 4, 5, . . . . (b) 10, 2, 25 , 2 25 , . . . . (c) 1,−1, 1,−1, . . . . (d) 0, 2, 4, 8, 16, 32, . . . . 7. What size of payments must be put into an account at the end of each quarter to establish an ordinary annuity that in 14 years will have a value of $50, 000 if the investment pays 12% compounded quarterly. 7*. You start investing $125 at the end of each month into an ordinary annuity earning 7% annually compounded monthly. How many years will it take for the annuity to be worth (a) $100, 000? (b) $200, 000?
