How many years would it take for a dollar to triple in value if it earns a 6 percent rate of return?
> Sketch the region enclosed by the given curves and find its area. y = x', y= 4x – x²
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у — 1/х, у — 0, х— 1, х — 4; about the x-axis
> Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. у —х+ 1, у— 0, х — 0, х — 2; about the x-axis
> Find the volume of the described solid S. The solid S is bounded by circles that are perpendicular to the x-axis, intersect the x-axis, and have centers on the parabola / e/
> Find the volume of the described solid S. The base of S is the region enclosed by y = 2 - x2 and the x-axis. Cross-sections perpendicular to the y-axis are quarter-circles. y=2-x?
> Find the volume of the described solid S. The base of S is the same base as in Exercise 58, but cross sections perpendicular to the x-axis are isosceles triangles with height equal to the base.
> Find the volume of the described solid S. The base of S is the region enclosed by the parabola y = 1 - x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.
> Find the volume of the described solid S. The base of S is the same base as in Exercise 56, but cross sections perpendicular to the x-axis are squares. Data from Exercise 56: Find the volume of the described solid S. The base of S is the triangular reg
> Find the volume of the described solid S. The base of S is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross-sections perpendicular to the y-axis are equilateral triangles.
> Find the volume of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 4y2 = 36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.
> Find the volume of the described solid S. The base of S is a circular disk with radius r. Parallel cross sections perpendicular to the base are squares.
> Sketch the region enclosed by the given curves and find its area. у — 12 — х?, у — х? — 6 y
> Find the volume of the described solid S. A tetrahedron with three mutually perpendicular faces and three mutually perpendicular edges with lengths 3 cm, 4 cm, and 5 cm
> Find the volume of the described solid S. a a a
> Find the volume of the described solid S. A pyramid with height h and rectangular base with dimensions b and 2b
> Find the volume of the described solid S. A frustum of a pyramid with square base of side b, square top of side a, and height h What happens if a = b? What happens if a = 0? a
> Find the volume of the described solid S. A cap of a sphere with radius r and height h
> Find the volume of the described solid S. A frustum of a right circular cone with height h, lower base radius R, and top radius r ード ーミー
> Find the volume of the described solid S. A right circular cone with height h and base radius r
> (a) A model for the shape of a bird’s egg is obtained by rotating about the x-axis the region under the graph of Use a CAS to find the volume of such an egg. (b) For a red-throated loon, a = 20.06, b = 0.04, c = 0.1, and d = 0.54. Graph
> (a) If the region shown in the figure is rotated about the x-axis to form a solid, use the Midpoint Rule with n = 4 to estimate the volume of the solid. (b) Estimate the volume if the region is rotated about the y-axis. Again use the Midpoint Rule wit
> A log 10 m long is cut at 1-meter intervals and its cross- sectional areas A (at a distance x from the end of the log) are listed in the table. Use the Midpoint Rule with n = 5 to estimate the volume of the log. x (m) A (m²) x (m) A (m²) 0.68 0.53 1
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. 4х + у? — 12, х—у
> A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cross-sections spaced 1.5 cm apart. The liver is 15 cm l
> Each integral represents the volume of a solid. Describe the solid.
> Each integral represents the volume of a solid. Describe the solid. " (o* – y") dy TT
> Each integral represents the volume of a solid. Describe the solid. "f', (1 – y°y° dy TT
> Each integral represents the volume of a solid. Describe the solid. [" sin x dx Jo
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y - x, y - xe' /2; about y = 3
> Use a computer algebra system to find the exact volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y = sin?x, y = 0, 0 < x< ™; about y = -1
> Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves. у 31+
> Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then use your calculator to find (approximately) the volume of the solid obtained by rotating about the x-axis the region bounded by these curves. у — In
> Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. (a)
> Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the region. х —D1 - у?, х-- у? — 1
> Find the area of the shaded region. yA (1, е), y=e* y=xe**
> Compare a municipal bond with a tax-deferred annuity. When would one be more attractive than the other?
> Using the table in Example 14.13 on page 442 providing a comparison of tax- advantaged structures, explain why the qualified pension plan and the Roth IRA seem to be particularly attractive investments.
> Why is a qualified pension plan such an attractive tax shelter?
> Assuming that you didn’t regard a stock that declined since you bought it particularly highly, why wouldn’t you want to take a loss in the current year?
> Sarah had unrealized long-term capital gains and Marcy had unrealized long-term capital losses at year-end. When should each sell her shares: the current year or the next year?
> State how taxes are relevant in five major financial planning areas.
> When would a mutual fund be more attractive than an annuity?
> Which plan is more likely to be attractive to a younger person, a defined benefit or a defined contribution plan?
> Explain the difference between a defined benefit and a defined contribution plan.
> Explain the relationship of life cycle theory to retirement planning.
> When it came to investments, Richard and Monica could agree on only one thing—that they would have a tough time reaching a decision on asset allocations and individual investments. Previously, Monica had deferred to Richard on investment matters. Given R
> Ann was offered an annuity of $20,000 a year for the rest of her life. She was 55 at the time, and her life expectancy was 84. The investment would cost her $180,000. What would the return on her investment be?
> Todd was asked what he would pay for an investment that offered $1,500 a year for the next 40 years. He required an 11 percent return to make that investment. What should he bid?
> Marcy placed $3,000 each year into an investment returning 9 percent a year for her daughter’s college education. She started when her daughter was two. How much had she accumulated by her daughter’s 18th birthday?
> Jason was promised $48,000 in 10 years if he would deposit $14,000 today. What would his compounded annual return be?
> What is the future value of an investment of $18,000 that will earn interest at 6 percent and fall due in seven years?
> What is the present value of a $20,000 sum to be given six years from now if the discount rate is 8 percent?
> Elena is in the 28 percent bracket and has the following real estate and non real-estate related costs. Nonmortgage interest and principal ……………………$ 4,000 Mortgage interest …………………………………………………15,000 Mortgage principal ………………………………………………….7,000 Real esta
> Given the following statistics, calculate the mortgage cost percent. Annual mortgage interest ……………………………………$ 9,000 Annual principal payment ……………………………………….2,000 Annual insurance and real estate taxes …………………..8,000 Yearly gross income …………………………………………
> How much would a person save by borrowing money at 6 percent for a home equity loan versus 18 percent for a credit card loan. Assume a marginal tax bracket of 30 percent.
> Monica continued to worry about the couple’s financial future. She began to question their investment in a home. She asked whether would be better to sell their home now and invest the proceeds. She estimated that the marketable securities would provide
> Martha has seven years remaining on her $160,000 mortgage, which has a 7.5 percent rate. She would have to pay $4,500 to refinance. Martha expects to live in the house for another five years. She is in the 33 percent marginal tax bracket and can earn 10
> Melinda has a 15-year fixed-rate mortgage for $150,000 at a 6.5 percent rate. Calculate her monthly mortgage payments.
> For the $8,000 loan John needed, he was given a choice of in loans with the following characteristics. a. $1,200 in interest paid at the end of the period. b. $1,200 in interest paid at the beginning of the period. c. $1,200 paid equally over the period
> Dorothy has the following projected cash flows: income, $65,000; fixed operating costs excluding interest, $44,000; variable outlays, $7,000; interest cost, $5,000; and repayment of debt, $6,000. Does Dorothy have high operating leverage? Calculate what
> Becky made a $30,000 investment in year 1, received a $10,000 return in year 2, $8,000 in year 3, $11,000 in year 4, and $9,000 in year 5. What was her internal rate of return over the five-year period?
> John had $50,000 in salary this year. If this salary is increasing 4 percent annually and inflation is projected to rise 3 percent per year, calculate the amount of return he will receive in nominal and real dollars in the fifth year.
> Kenneth made a $20,000 investment in year 1, received a $5,000 return in year 2, made an $8,000 cash payment in year 3, and received his $20,000 back in year 4. If his required rate of return is 8 percent, what was the net present value of his investment
> What is the difference in future value between savings in which $3,000 is deposited each year at the beginning of the period and the same amount deposited at the end of the period? Assume an interest rate of 8 percent and that both are due at the end of
> What is the difference in amount accumulated for a $10,000 sum with 12 percent interest compounded annually versus one compounded monthly over a one-year period?
> Aaron has $50,000 in debt outstanding with interest payable at 12 percent annually. If Aaron intends to pay off the loan through four years of interest and principal payment, how much should he pay annually?
> Unlike Richard, Monica remained very concerned about their financial future. Specifically she was fearful that the couple would not have enough money to retire comfortably as they had expected. She asked whether she should postpone or eliminate one impro
> How many years would it take for $2,000 in savings a year earning interest at 6 percent to amount to $60,000?
> Earnestos was an accountant. He had a good job with a major accounting firm with a bright future. He also had a huge spending habit. He had $15,000 of credit card debt and as adding to it each month. His wife didn’t know about it and believed that he ha
> Abby had the following statistics. Calculate the gross savings percentage. Net cash flow …………………………………………………$6,000 Nondiscretionary expenses…………………………….. 35,000 Discretionary expenses ……………………………………..8,000 Targeted retirement savings ……………………………..5,000
> Sharon had gross income of $120,000 and nondiscretionary expenses of $32,000. She also had discretionary expenses of $10,000, and her capital expenditures on leisure items were $5,000. What is her discretionary payout percentage?
> Jamie had the following figures over the past four years. a. Calculate the nondiscretionary cost percentage and what the change in the ratio demonstrates over time. b. Calculate the discretionary cost percentage and what the change demonstrates over ti
> Using the following statistics, calculate Jackson’s current and emergency fund ratios. Current assets ……………………………………..$2,000 Current liabilities …………………………………….1,000 Liquid assets ………………………………………….8,000 Marketable securities ……………………………20,000 Monthly ho
> April made $50,000 in year 1 and $60,000 in year 2. She had the following yearly outflows: Calculate April’s operating cash flow and net cash flow for each year. Year 1 Year 2 Nondiscretionary Discretionary Capital expenditures De
> Magdalena, age 35, has $72,000 accumulated in savings. She projects she will save $23,000 a year until her retirement at age 67. Her current cost of living is $100,000. In retirement, she will receive $31,704 per year in Social Security and $20,000 in pe
> The Smiths had $110,000 in savings at age 51. They had a desired retirement age of 65. They want to fund through age 92. Assume a 4 percent inflation rate and a 5 percent after tax rate for investment both pre- and postretirement. They have household inc
> Frank, age 28, wants to calculate his resources in real (inflation-adjusted) terms. Calculate the amount of resources made available by age 65 retirement if $18,000 a year is saved. Assume that outflows from ages 65 to 90 are at the rate of $27,000 a yea
> Brad and Barbara made an appointment to see me concerning their own financial situation. They were a newly married couple in their early 20s. Barbara came from a family whose parents had children early in their lives; the women were full-time mothers unt
> Eleanor needs $40,000 a year to live on in retirement net of the income she will receive. She will be retiring in 22 years and is funding for a 25-year retirement. The inflation rate is expected to be 3.5 percent a year and the after-tax return on her in
> If the investment rate of return is 7 percent after tax and the inflation rate is 4 percent, find the blended rate of return.
> Y Co. has a projected dividend of $2.00, has a required rate of return of 8 percent, and is expected to grow 6 percent a year. Solve for its anticipated stock price.
> Pamela bought a bond for $926 with a face value of $1,000 and an annual coupon of $50. If the bond matures in 18 years, what is her yield to maturity?
> If a bond has annual interest payments of $50 and a par value of $1,000, with six years to maturity, what is its current market value if bonds like it are currently offering a 7 percent yield?
> Beth bought a bond at $800 with annual coupon payments of $40. If the bond is due in nine years and has a par value of $1,000, what is her yield to maturity under both the approximate method and the more exact method.
> Multicolor Corp. had an annual coupon of $60.00, a face value of $1,000, and a market value of $840. Calculate the coupon yield and the current yield.
> Tricontinental’s bond had a liquidity risk of 1 percent, a maturity risk of 2 percent, a pure rate of return of 1.5 percent, and an inflation premium of 4.0 percent. If the expected bond yield was 17 percent, what was the default risk? What does your ans
> Maurice gave $20,000 to charity each year. He had $20,000 in stock that cost him $14,000 to buy. Assuming he is in the 23 percent marginal tax bracket for capital gains, how much will he save by donating the stock directly to charity?
> Sophia inherited 1,000 shares of IBM that her father’s parents bought for her when she was a child. The father’s cost was $2 per share at the time of purchase and $84 per share at the time of his death. Sophia sold them at $86 per share. Calculate the to
> Brad and Barbara say they use credit cards all the time. They always intend to pay them off by the end of the month, but they often don’t. In fact, their credit card debt has been rising recently. Required: 1. Is this pattern common? 2. What is your rec
> John inherited $1 million in an IRA, which comprised the entire estate from his father, who had recently died. He promptly withdrew the funds. The appropriate marginal tax rate was 39.6 percent. Was there any tax due? If so, how much? Assume it was $1 mi
> Compare a pretax $10,000 sum placed in bonds yielding 6 percent in a qualified pension with an investment in a municipal bond yielding 5 percent. The municipal bond sum deposited was made with after-tax dollars on the same pretax $10,000. The marginal ta
> The estimated value of a real estate asset in a financial statement prepared by a Certified Financial Planner licensee should be based upon the a. Basis of the asset, after taking into account all straight-line and accelerated depreciation. b. Client’s e
> Arrange the following financial planning functions in the logical order in which these functions are performed by a professional financial planner. 1. Interview clients, identify preliminary goals 2. Monitor financial plans 3. Prepare financial plan 4. I
> You receive a phone call from someone you have not spoken to recently. The caller is excited, having just heard that a brand new mutual fund is positioned to deliver large gains in the coming year. The caller wishes to purchase shares of the fund through
> What are the differentiating factors between regular annuity and annuity due?
> The cost of time is a noncash charge, so why is it important?
> What types of investments are suited to retirement planning at age 67 assuming the person is 55 and has an average risk tolerance?
> What kinds of investments are best suited to saving for the down payment on a house to be made in three years?
> Explain why under CAPM company risk can be diversified away.
> What is involved in establishing the cap rate?
