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linear algebra

Questions and Answers of Linear Algebra

Michelle took out a $370,000 30-year adjustable rate mortgage with a 3.8% initial 6-month rate. The amortization table for the initial rate period is shown. After the first 6 months, the rate went up
Calculate the missing amounts in the amortization table which shows extra payments toward the principal made each month.
Adam is taking out a $197,000 mortgage. His bank offers him an APR of 7.45%. He wants to compare monthly payments on a 20- and a 30-year loan. Find, to the nearest ten dollars, the difference in the
Brianna just signed a lease on a rental apartment. The current rent is $1,330 per month, and she estimates a 6% increase each year. Use her estimate to predict the sum of the next five years' worth
The Bricely Family borrowed $176,000 from Glen Bank several years ago when they bought their co-op for $246,000. The price dropped d dollars since they bought it. After making years of payments and
Explain how the quote can be interpreted.
Jack contributed $400 per month into his retirement account in pre- tax dollars during the last tax year. His taxable income for the year was $62,350. He files taxes as a single taxpayera. What would
Mark is an accountant who has been contributing to his retirement account for the last 15 years with pre-tax dollars. The account com- pounds interest semi-annually at a rate of 5%. He contributes X
Jhanvi is a 40-year-old executive for a department store. She files taxes as head of household. She needed to withdraw $45,000 from her tax-deferred retirement account to put a down payment on a new
Nelson makes $120,000 per year. His employer offers a 401k plan in which they will match 40% of his contributions up to a maximum of 7% of his annual salary. His employer allows contributions up to a
Mike makes Y dollars per year. His company offers a matching retirement plan in which they agree to match M percent of his contributions up to P percent of his salary. Write an algebraic expression
Ricky is 35 years old. He plans to retire when he is 63. He has opened a retirement account that pays 3.2% interest compounded monthly. If he makes monthly deposits of $400, how much will he have in
Jay just graduated from college and he has decided to open a retirement account that pays 1.75% interest compounded monthly. If he has direct deposits of $100 per month taken out of his paycheck, how
At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an APR of 4%. She made no further deposits. After 25 years, she decided to withdraw
A taxpayer who pays 22% in taxes each year has these two accounts. Account 1: $10,000 is placed in a tax-deferred account that pays 5% interest compounded annually for 25 years.Account 2: $10,000 is
Laura has been contributing to a retirement account that pays 4% interest with pre-tax dollars. This account compounds interest monthly. She has put $500 per month into the account. At the end of 10
Fiona opened a retirement account that has an annual yield of 6%. She is planning on retiring in 20 years. How much must she deposit into that account each year so that she can have a total of
John is 60 years old. He plans to retire in two years. He now has $400,000 in a savings account that yields 2.9% interest compounded continuously. He has calculated that his final working year's
Bob can afford to deposit $400 a month into a retirement account that compounds interest monthly with an APR of 3.9%. His plan is to have $200,000 saved so that he can then retire. Approximately how
Interpret the quote in the context of what you know about American history and/or challenges facing senior citizens.
Dominique is single. She is filling out the Social Security worksheet so she can determine the amount of her Social Security benefits that she will pay federal income tax on. Fill in the following
Roberta's Social Security full retirement benefit is $2,101. She started collecting Social Security at age 64, and her benefit is reduced since she started collecting before age 67. Find her
Linda and Rob are married filing a joint Form 1040. Rob is collecting Social Security, but Linda is not. They are filling out the Social Security worksheet (shown in Exercise 11) so they can
You can receive Social Security payments for being disabled even if you have not retired or reached age 62. You need a certain number of Social Security credits to qualify for this.• If you become
In 2008, the maximum taxable income for Social Security was $102,000 and the tax rate was 6.2%.a. What is the maximum Social Security tax anyone could have paid in the year 2008?b. Randy had two jobs
In a certain year, the maximum taxable income for Social Security was x dollars and the tax rate was 6.2%. a. What is the maximum Social Security tax anyone could have paid in that year? b. Paul had
Stacy was a stay-at-home mom for most of her adult life. At age 46, she started working outside the home. Each year she earns the maxi- mum number of Social Security credits. Until what age must she
Rachael turned 62 in 2007.a. Compute her Social Security full retirement benefit if her average monthly salary over her 35 highest-paying years was $3,100.b. If she starts collecting her benefit at
Michelle turned 62 in 2007. She earned an average of x dollars per month (adjusted for inflation) over her highest-paying 35 years, where x > 4,100. Express her Social Security full retirement
Explain how that quote can be interpreted in light of what you have experienced in this lesson.
Grant's employer offers a pension plan that calculates the annual pension as the product of the final average salary, the number of years of service, and a 2% multiplier. His employer uses a graded
Peterson Products calculates its pension benefits as follows:Years of service × 1.98% multiplier × Average of last two annual salariesWhat is Mary's monthly pension benefit if she worked for
Jamal is retiring after working 45 years for the same company. The company pays a monthly retirement benefits of $35 for each year of service less than 20 years. The benefit increases by 1 / 10% for
Sunshine Living calculates its pension benefits as follows: Years of service × 2.25% multiplier × Average of last five annual salaries. What is Killian's annual pension benefit if he worked for
Sara works for the City of Northbeck. The city calculates an employee's pension according to the following formula. • Determine the average of the highest 3 years of annual earnings. • Determine
Carmen is a teacher in the district who began working there in 1995 and will retire in 2010 after 15 years of service. In the 2007-08 school year, she made $60,000. She received a 2% cost of living
Ralph is a district employee. His final three years of annual salaries were D, E, and F dollars. If he worked for A years (where A > 15), write an algebraic expression that represents his annual
Janet is retiring after working for a major department store for 20 years. The company offered her a flat retirement benefit of $50 per year for each year of service. a. What was her monthly income
Martina's employer offers an annual pension benefit calculated by multiplying 2.35% of the career average salary times the number of years employed. Here are Martina's annual salaries over the last
The Morning Sun offers employees 1.65% of the average of their last three years of annual compensation for each year of service. Ramon began working for the Morning Sun in 1988. He retired in 2010.
Office Industries uses a final average formula to calculate employees' pension benefits. The calculations use the salary average of the final four years of employment. The retiree will receive an
Interpret the quote in the context of what you have learned throughout your financial algebra course.
Johan took out a 10-year term policy with a face value of x dollars. Over the lifetime of the policy, he pays monthly payments of m dollars. He dies after making payments for 3 1 1 / 4 years. a. How
The Durham Insurance Company sells a five-year term insurance policy with face value of $100,000 to a 47-year-old man for a monthly premium of $63. The mortality table is given below.d. What is the
Life insurance companies take risks much like arcade game owners take risks. Mollie has a booth on a popular beach boardwalk. She charges $2 per game. Winners receive a $5 prize. The probability of
Premiums for the Sun-Belt Insurance Company are given in the table. Find the annual premiums for $250,000 of the following Sun- Belt life insurance policies.a. A 10-year life insurance policy
New City Insurance Company offers a term life insurance policy with a renewable annual premium. The first year premium is $140. Premiums increase 6% each year. a. What will the premium be in the
Jonathan has a universal life insurance policy with a face value of $500,000. The current cash value of the policy is $11,260. Jonathan wants to stop paying premiums for a few months while he
Use the mortality table below to answer parts a-f.a. The life expectancy column gives the number of years a person of that age is expected to live. What is the life expectancy for a 67-year-old
Use the definition of the greatest integer function to evaluate each of the following.a. [55.9]b. [55.001]c. [0.65]d. [−34.11]e. [16 3 / 14]f. [−8.21]g. [19]h. [−0.45]i. [- 8 1 / 2]j. [ 2 / 3]
Zeke has a universal life insurance policy with a face value of $200,000. The current cash value of the policy is x dollars. The premium is m dollars per month. He is going to use the cash value to
In 2009, the maximum taxable income for Social Security was $106,800. The FICA tax rate was 6.2%.a. What is the maximum anyone could have paid into FICA tax in the year 2009?b.
Use the mortality table to answer parts a and b.a. If the company insures 10,000 63-year-old males, how many are expected to die before their 64th birthday? Round to the nearest integer.b. Based on
The Lieberman Insurance Company sells a 5-year term insurance policy with face value of $250,000 to a 39-year-old man for an annual premium of $973. The mortality table is given below.a. Assume the
Deanna is 62 years old. She plans to retire in 3 years. She has $300,000 in a savings account that yields 2.25% interest com- pounded daily. She has calculated that her final working year's salary
Mitch opened a retirement account that has an annual yield of 4.2%. He is planning on retiring in 13 years. How much must he deposit into that account each year so that he can have a total of
Hillary's employer offers an annual pension benefit, for employees that have worked for the company for more than 10 years. The benefit is calculated by multiplying 5.08% of the career average salary
Hannah contributed $300 per month into her retirement account in pre-tax dollars during the last tax year. Her taxable income for the year was $72,000. She files taxes as a single taxpayer.a. What
Regina is a 45-year-old supervisor for a communications company. She files taxes as married filing separately. She withdrew $50,000 from her tax-deferred retirement account to pay off her loans.
Petra's employer offers an annual pension benefit calculated by multiplying 2.46% of the career average salary times the number of years employed. Here are Petra's annual salaries over the last 16
NuEditions Book Company uses a final average salary formula to calculate an employee's pension benefits. The amount used in the calculations is the salary average of the final 3 years of employment.
In 1990, the amount of earnings required to earn one Social Security credit was $520. In the tax year 1990, Maggie earned $187 biweekly. How many Social Security credits did she earn in 1990?
Anna turned 62 in 2007, and she is computing Social Security benefits. Using the formula from Example 3 in Lesson 9-2, compute her Social Security full retirement benefit if her average monthly
Nick's annual salary is $90,000. His employer matches his 401k contributions at $0.75 for each dollar up to 8% of his annual salary. Nick contributes $350 from each biweekly paycheck to his 401k
Juanita's Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the
Charleen is single. She is filling out the Social Security worksheet shown on page 451 so she can determine the amount of her Social Security benefits that she will pay federal income tax on. The
Reliable Insurance Company offers a term life insurance policy with a renewable annual premium. The first year premium is $795. Premiums increase by 4.1% each year. What will premiums be in the nth
Jessica's parents are always telling her to turn off the lights when she leaves a room. A light bulb requires 75 watts to run when it is turned on. The fixture in Jessica's room requires four of
Ron Sargeant's electric bill from the Longwood Power Authority is shown. If his meter reading for December 17 is 52,344, find the total charges for the December bill. Include all rates and charges as
Last year, the Forrester family spent $1,882.56 for electricity. They are opting to use balanced billing for next year.a. What will their monthly payment be under balanced billing?b. Last year, they
The Zlotnick family pays $223 per month for electricity under balanced billing. At the end of the year, they had used more electricity than the balanced billing covered, and they owed the utility
The Waldner family paid their electric bill using balanced billing all last year. The monthly payment was mx dollars. At the end of the year, the electric company told them they had a credit of cx
A certain appliance uses w watts to run. If you run it for m minutes, and the cost per kilowatt-hour is c, the cost of running the appliance for m minutes is given by the formulaFind the cost of
A large appliance such as a water heater is only running when it has clicked on and is actually heating water. The time your water heater is on varies according to how much you do laundry, take
Air conditioners are rated by BTUs. You learned about BTUs in Lesson 8-2, Example 6. One watt-hour is equivalent to 3.413 BTUs per hour.a. How many BTUs per hour are equivalent to a kilowatt-hour?b.
What is the meter reading, in ccf, indicated by each of the gas meters shown?a.b. c. d.
Bill Heckle's last electric bill is shown below.a. What was the previous reading? b. What is the present reading? c. How many kilowatt-hours of electricity did Bill use during the service period
Home heating oil is sold by the gallon. Last winter, the Romano family used 370 gallons of oil at a price of $3.91 per gallon. If the price increases 9% next year, what will their approximate heating
The PA system at North High School requires 400 watts when it is switched on. How much would it cost to run for 3 hours, at a cost of $0.10 per kilowatt-hour?
The Zwerling family installed central air conditioning in their house this summer. They are comparing the electric bills of this summer and last summer. The data is shown.a. What was the total
A certain appliance requires 225 watts when it is switched on. How much would it cost to run for m minutes, at a cost of d dollars per kilowatt-hour? Express your answer algebraically.
Interpret the quote in the context of what you know about the standard of living throughout the world.
The Fi-Zone cable TV/Internet/phone provider charges $100 per month for all three services for a new customer's first year. Tobi normally pays p dollars for her monthly home phone service, i dollars
Throughout this lesson you have used the greatest integer function y = [x]. Use your graphing calculator to view the graph of this function and find the y-coordinate for each of the following
A pay phone at a shopping mall charges $0.68 for the first four minutes and $0.21 for each extra minute (or part of a minute).a. Find the cost of a 10-minute call on this phone.b. Find the cost of a
A phone company set the following rate schedule for an m-minute call from any of its pay phones.a. What is the cost of a call that is under six minutes?b. What is the cost of a 14-minute call?c. What
The Tell-All Phone Company charges $0.58 for the first two minutes and $0.21 for each extra minute (or part of a minute). Express their rate schedule as a piecewise function. Let m represent the
Phone companies itemize charges on monthly bills. There are several fees, call surcharges, and taxes. There could be charges for maintenance of the phone wiring within the home. These charges inflate
A local cable TV/Internet/phone provider charges new customers $99 for all three services, per month, for the first year under their "3 for 99" promotion. Joanne normally pays $54 for her monthly
A cable TV/Internet/phone provider charges Janet $90 per month for all three services. In addition, Janet's monthly bill for cell phone calls and text messages averages $77 per month.a. What does
Text-Time charges $25 for a texting plan with 300 text messages included. If the customer goes over the 300 messages, the cost is $0.10 per message. They have an unlimited plan for $48 per month.a.
Explain how that quote can be interpreted in light of what you have learned in this lesson.
Construct a bar graph for the September budget category "Personal Items" using the following amounts: Haircut: $20, Clothing purchases: $60, Books: $20, Newspapers/Magazines: $65, online
Aida created the following double bar graph. It illustrates the actual amount spent this year for household expenses per month and the budgeted amounts for the following year. The following year's
Mark works at two jobs. His primary job is a commission-paid job. Therefore, his monthly income from this job varies. His secondary job has a fixed monthly income. His quarterly dividend checks and
Rich budgets $2,500 in expenses for the month of January. He constructed the two graphs below.Using prior year's data and the budget he has created, he has budgeted the transportation category for
Under his household expense budget category, Mark has allocated $60 per month for pet food. He can purchase wet food in a can for $1.50 per can or dry food in a bag for $3 per bag.a. Determine a
A consumer budgets $480 per month for transportation. She has determined that the cost of a round-trip train ride is $4 and the cost of each round-trip car ride (factoring in gas, oil, etc.) is $3.a.
Create a year-long budget check-off matrix to chart the following transportation related expenses: Fuel: monthly; Insurance: quarterly; Servicing: every three months; Car wash: bimonthly; Parking:
Create a year-long budget matrix to chart these expenses: Savings: $600 bimonthly (starting in January); Retirement account: $2,000 quarterly; Checking account: $1,000 semi-monthly; Credit card: $500

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