.Solve the following questions.

(1) The force of interest changes from moment to moment according to the formula ?t = 0.10e 0.012t . You invest $ 1,000 at time 0. Find the accumulated value at time 6.

(2) The force of interest changes from moment to moment according to the formula ?t = 0.008t 2 , where t is measured in years. You expect to receive a payment of 500,000 at time 5. Find the present value of this payment at time 0.

(3) Find the present value of a 30-year annuity-immediate which pays $2,000 each year. Assume an effective annual interest rate of 8%.

(4) Find the present value of a 20-year annuity-due which pays $4,000 each year. Assume that the effective annual interest rate is 6%.

(5) Suppose that Abby offers to pay you $1,000 at the end of each year for the next 10 years. Ben offers to pay you $10,000 at time t. The effective annual interest rate is 7%. Find the value of t (in years, to two decimal places) such that you are indifferent between Abby's and Ben's offers.

(6) Suppose that Melissa offers to pay you $2,000 at the end of each year for the next 5 years. Matthew offers to pay you $7,000 at time t. The effective annual interest rate is 9%. Find the value of t (in years, to two decimal places) such that you are indifferent between Melissa's and Matthew's offers. Interpret your answer. 2

(7) An annuity pays 10,000 every year for 30 years. Find the accumulated value of this annuity 3 years after the last payment. Assume that the effective annual interest rate is 10%.

(8) An annuity pays 5,000 every year for 25 years. Find the present value of this annuity 2 years before the first payment. Assume that the effective annual interest rate is 12%.

(9) A perpetuity will pay X every year. The effective annual interest rate is 7.5%. The present value of this perpetuity 4 years before the first payment is 125,000. Find X.

(10) Suppose you deposit $20,000 at the end of each of the next 30 years into a retirement account. Immediately after your last deposit, you take the entire accumulated value in your account and purchase a 20-year annuity, which will pay you X at the beginning of each year for 20 years. The price of this 20-year annuity is equal to the present value (at the time you purchase the annuity) of the 20 annual cash flows. The effective annual interest rate throughout the entire 50-year period is 10%. Find X.

Problems (Solusand to problemis mariged * appear at the bock of this book. Problems adapted to one calculus in availabit saint at 1. Which assumption about consumer preferences does by three different consumers (Augn, Barbara, and each of the following individuals violate? Camina), holding everything else constant: . Adam likes basketball more than football; Auon Football more than baseball; and baseball more Barbara Camira than basketball. b. Christina prefers prune juice to orange juice but 02 cannot decide how she feels about grapefruit juice. C. Blake likes superhero comic books but prefers 5 comic books to 10 comic books. 54 2. By assumption, individual preferences must be tran- sitive so that if A is preferred to B, and B is preferred to C. then A is preferred to C. Suppose that Marsha, 17 5 Jan, and Cindy individually have transitive prefer- ences over three goods: oranges, apples, and pears. Compute the marginal utility of X for each of the If Marsha, Jan, and Cindy were to vote on whether three consumers at each level of X. to name oranges, apples, or pears the "fruit of the b. Based on the data in the table, can you tell month," show that it is possible the preferences for whether any of these consumers are violating any the group might not be transitive. of the standard assumptions about preferences? 3. Draw two indifference curves for each of the follow- c. Is it possible that any of these three consumers ing pairs of goods. Put the quantity of the first good have the same preferences, and that columns for the on the horizontal axis and the quantity of the second three consumers differ only because of the arbitrary good on the vertical axis. units that are used to measure utility? Explain Paul likes pencils and pens, but does not care $6. A consumer's utility function is given by U- XY. which he writes with where MU, - F and MU, = X. Rhonda likes carrots and dislikes broccoli. a. What is the utility derived from 1 unit of X and C. Emily likes hip-hop iTunes downloads and 2 units of Y? What is the utility derived from doesn't care about heavy metal downloads. 2 units of X and I unit of F? What is the utility d. Michael only likes dress shirts and cufflinks in 1 derived from 5 units of X and 2 units of Y? to 2 proportions. b. How does the consumer rank the following e. Carlene likes pizza and shoes. bundles? *4. Suppose that John is indifferent between consuming Bundle Quantity of I Quantity of F bundle A. which consists of 4 apples and 1 peach, and bundle B, which consists of 4 peaches and A 2 1 apple. If John were given the choice between bun- 10 dle A and bundle C, which contained 3 peaches and 2 apples, which should be pick? (Hint: Draw an 5 indifference curve or two.) 3 2 5. The following table displays the total utility ((X ) that 2 3 comesponds to the number of units of X consumedMAT 166 - Pre-Calculus Writing Assignment I Students will be expected to answer all questions with the whole story. Perform each task on your paper. If you are asked to explain or define, be sure to use complete sentences, Sentence fragments are meaningless in technical writing. The intent should be to inform the reader, and to convince the reader of the knowledge and competence of the author. Answer the following questions in the order they are given. Answers should be organized on a separate sheet of paper. Answers may be hoped, hand written or a combination of both. If answers to questions are not numbered for lettered), it will be assumed that question I was answered and no other. This assignment is intended as a condensed review of functions. There is a recommended video that may aid in the completion of this assignment, but you may use any resource to aid in the completion of this assignment. Be sure to use a trusted source, and cite any source that you used. If you quote a source, paraphrase the quote in your own words. 1. Read all the directions for this assignment and copy the most important instruction as your answer to this question. 2. Watch the video https /www.youtube.com/watch/v .HOggysawWg and write your favorite color as the answer to this question. 3. Create or find a definition of a function. Include a definition of "domain" and "range" in the answer to this question. (It is recommended that the words "relation" or "pairing" be used in the definition.) (see page 137,138) Use the previous definition of function to explain the "vertical line test" and why it works. Note: A fest and a definition are not the same. 5. Tell why the trigonometric functions adhere to the algebraic definition of a function, and describe the "inputs" and "outputs" of any trigonometric function. 6. Create or find a definition of a "one-to-one function". (p 357) 7. Use the previous definition to explain the "horizontal line test" and why it works. Note: A rest and a definition are not the same 8. Create or find a definition of "inverse functions". (p 359) 9. Given that the function /(* has an inverse function . (F); a. If /(2)=120 , Find / (120) b. If the domain of /(x) is xE[0, 1000) . what is the range of (E)? c. If the domain of ()represents time in years after 2010, and the domain of / (*) represents the population of Ourtown, write a sentence to interpret i. f (2)=120 ii. f (500) =7 / (x1=x+5 10. Let 7 and g(x)=7x-5 a. Find (9 (x) and (9 f)(x ) b. Come to a conclusion about the relationship between the functions f(x ) and g(x) explain how you arrived at the conclusion. and 1 1. What is the most important concept you have learned remembered by doing this assignment