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mathematics
calculus
Mathematical Applications for the Management Life and Social Sciences 11th edition Ronald J. Harshbarger, James J. Reynolds - Solutions
Sofia can deposit $350 at the beginning of each month into an account that earns 4.2% compounded monthly. How long before the account contains $17,000? (a) State whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
Mr. Gordon plans to invest $300 at the end of each month in an account that pays 9%, compounded monthly. After how many months will the account be worth $50,000? (a) State whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
For 3 years, $400 is placed in a savings account at the beginning of each 6-month period. If the account pays interest at 10%, compounded semiannually, how much will be in the account at the end of the 3 years? (a) State whether the problem relates to an ordinary annuity or an annuity due, and
Grandparents plan to open an account on their grandchild's birthday and contribute each month until she goes to college. How much must they contribute at the beginning of each month in an investment that pays 12%, compounded monthly, if they want the balance to be $180,000 at the end of 18
How much money should a couple deposit at the end of each month in an investment plan that pays 7.5%, compounded monthly, so they will have $800,000 in 30 years? (a) State whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
Jane Adele deposits $500 in an account at the beginning of each 3-month period for 9 years. If the account pays interest at the rate of 8%, compounded quarterly, how much will she have in her account after 9 years? (a) State whether the problem relates to an ordinary annuity or an annuity due, and
A company establishes a sinking fund to discharge a debt of $750,000 due in 8 years by making equal semiannual deposits, the first due in 6 months. If the investment pays 12%, compounded semiannually, what is the size of the deposits? (a) State whether the problem relates to an ordinary annuity or
A sinking fund is established by a working couple so that they will have $60,000 to pay for part of their daughter's education when she enters college. If they make deposits at the end of each 3-month period for 10 years, and if interest is paid at 12%, compounded quarterly, what size deposits must
A property owner has several rental units and wants to build more. How much of each month's rental income should be deposited at the beginning of each month in an account that earns 6.6%, compounded monthly, if the goal is to have $100,000 at the end of 4 years? (a) State whether the problem
Suppose a recent college graduate's first job allows her to deposit $100 at the end of each month in a savings plan that earns 9%, compounded monthly. This savings plan continues for 8 years before new obligations make it impossible to continue. If the accrued amount remains in the plan for the
Suppose a young couple deposits $1000 at the end of each quarter in an account that earns 7.6%, compounded quarterly, for a period of 8 years. After the 8 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 8 years in the account and
A small business owner contributes $3000 at the end of each quarter to a retirement account that earns 8% compounded quarterly.(a) How long will it be until the account is worth $150,000?(b) Suppose when the account reaches $150,000, the business owner increases the contributions to $5000 at the
A young executive deposits $300 at the end of each month for 8 years and then increases the deposits. If the account earns 7.2%, compounded monthly, how much (to the nearest dollar) should each new deposit be in order to have a total of $400,000 after 25 years?
The figure shows a graph that compares the future values, at 8% compounded annually, of an annuity of $1000 per year and one of $1120 per year.(a) Decide which graph corresponds to which annuity.(b) Verify your conclusion to (a) by finding the value of each annuity and the difference between them
The figure shows a graph that compares the future values, at 9% compounded monthly, of an annuity of $50 per month and one of $60 per month.(a) Decide which graph corresponds to which annuity.(b) Use the graph to estimate (to the nearest 10 months) how long it will be before the larger annuity is
1. Find the future value of an annuity of $1300 paid at the end of each year for 5 years, if interest is earned at a rate of 6%, compounded annually? 2. Find the future value of an annuity of $5000 paid at the end of each year for 10 years, if it earns 9%, compounded annually?
1. Find the future value of an ordinary annuity of $80 paid quarterly for 3 years, if the interest rate is 8%, compounded quarterly? 2. Find the future value of an ordinary annuity of $300 paid quarterly for 5 years, if the interest rate is 12%, compounded quarterly?
1. Find An: An = 1300 [1 - (1 + 0.04)-30/0.04]2. Find An: An = 2550 [1 - (1 + 0.01)-120/0.01]3. Find R: 135,000 = R[1 - (1 + 0.005)-360/0.005]4. Find R: 25,000 = R[1 - (1 + 0.02)-20/0.02]
A personal account earmarked as a retirement supplement contains $242,400. Suppose $200,000 is used to establish an annuity that earns 6%, compounded quarterly, and pays $4500 at the end of each quarter. How long will it be until the account balance is $0?
A professional athlete invested $2.5 million of a bonus in an account that earns 6.8%, compounded semiannually. If $120,000 is to be withdrawn at the end of each six months, how long will it be until the account balance is $0?
Suppose that a 25-year government bond has a maturity value of $1000 and a coupon rate of 6%, with coupons paid semiannually. Find the market price of the bond if the yield rate is 5% compounded semiannually. Is this bond selling at a discount or at a premium?
Suppose that a 10-year corporate bond has a maturity value of $25,000 and a coupon rate of 7%, with coupons paid semiannually. Find the market price of the bond if the yield rate is 8% compounded semiannually. Is this bond selling at a discount or at a premium?
The figure shows a graph that compares the present values of two ordinary annuities of $1000 annually, one at 8% compounded annually and one at 10% compounded annually.(a) Determine which graph corresponds to the 8% rate and which to the 10% rate.(b) Use the graph to estimate the difference between
1. The figure shows a graph that compares the present values of two ordinary annuities of $800 quarterly, one at 6% compounded quarterly and one at 9% compounded quarterly.(a) Determine which graph corresponds to the 6% rate and which to the 9% rate.(b) Use the graph to estimate the difference
Find the present value of an annuity due that pays $3000 at the beginning of each quarter for the next 7 years. Assume that money is worth 5.8%, compounded quarterly?
Find the present value of an annuity due that pays $25,000 every 6 months for the next 212 years if money is worth 6.2%, compounded semiannually?
What amount must be set aside now to generate payments of $50,000 at the beginning of each year for the next 12 years if money is worth 5.92%, compounded annually?
Suppose an annuity will pay $15,000 at the beginning of each year for the next 7 years. How much money is needed to start this annuity if it earns 7.3%, compounded annually?
A year-end bonus of $25,000 will generate how much money at the beginning of each month for the next year, if it can be invested at 6.48%, compounded monthly?
A couple inherits $89,000. How much can this generate at the beginning of each month over the next 5 years, if money is worth 6.3%, compounded monthly?
An insurance settlement of $1.5 million must replace Trixie Eden's income for the next 40 years. What income will this settlement provide at the end of each month if it is invested in an annuity that earns 8.4%, compounded monthly? (a) Decide whether the problem relates to an ordinary annuity or
A local library receives a bequest of $100,000 from a prominent local family. How much will this provide at the beginning of each 3-month period for the next 212 years if money is worth 7.4% compounded quarterly? (a) Decide whether the problem relates to an ordinary annuity or an annuity due, and
A company wants to have $40,000 at the beginning of each 6-month period for the next 412 years. If an annuity is set up for this purpose, how much must be invested now if the annuity earns 6.68%, compounded semiannually? (a) Decide whether the problem relates to an ordinary annuity or an annuity
Is it more economical to buy an automobile for $29,000 cash or to pay $8000 down and $3000 at the end of each quarter for 2 years, if money is worth 8% compounded quarterly? (a) Decide whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
Dr. Jane Kodiak plans to sell her practice to an HMO. The HMO will pay her $1.5 million now or will make a $500,000 partial payment now and make additional payments of $140,000 at the end of each year for the next 10 years. If money is worth 6.5%, compounded annually, is it better to take $1.5
As a result of a court settlement, an accident victim is awarded $1.2 million. The attorney takes one-third of this amount, another third is used for immediate expenses, and the remaining third is used to set up an annuity. What amount will this annuity pay at the beginning of each quarter for the
Recent sales of some real estate and record profits make it possible for a manufacturer to set aside $800,000 in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half-year for the next 3 years if the fund earns 7.7%, compounded
A $2.4 million state lottery pays $10,000 at the beginning of each month for 20 years. How much money must the state actually have in hand to set up the payments for this prize if money is worth 6.3%, compounded monthly? (a) Decide whether the problem relates to an ordinary annuity or an annuity
How long will an account worth $2.2 million provide $10,000 at the end of each month, if money is worth 5.4% compounded monthly? (a) Decide whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
A college class's 25th reunion gift is $8.6 million. How many semiannual payments of $250,000 will this provide at the beginning of each 6-month period if money is worth 4.4% compounded semiannually? (a) Decide whether the problem relates to an ordinary annuity or an annuity due, and then (b)
A used piece of rental equipment has 212 years of useful life remaining. When rented, the equipment brings in $800 per month (paid at the beginning of the month). If the equipment is sold now and money is worth 4.8%, compounded monthly, what must the selling price be to recoup the income that the
As a result of a court settlement, a financial firm agreed to pay $13.4 million to Ford Motor Company, with $10 million of it going to a Ford charitable trust (Source: The New York Times). If the trust invested this money at 6.3%, compounded annually, how much could be awarded to worthwhile
As the contestant with the longest winning streak in the history of Jeopardy, Ken Jennings won more than $2.5 million. Suppose he invested $1.5 million in an ordinary annuity that earned 7.2%, compounded monthly. How much would he receive at the end of each month for the next 20 years? (a) Decide
Suppose Becky has her choice of $10,000 at the end of each month for life or a single prize of $1.5 million. She is 35 years old and her life expectancy is 40 more years. (i) Find the present value of the annuity if money is worth 7.2%, compounded monthly. (ii) If she takes the $1.5 million, spends
Juanita Domingo's parents want to establish a college trust for her. They want to make 16 quarterly withdrawals of $2000, with the first withdrawal 3 months from now. If money is worth 7.2%, compounded quarterly, how much must be deposited now to provide for this trust? (a) Decide whether the
A retiree inherits $93,000 and invests it at 6.6%, compounded monthly, in an annuity that provides an amount at the end of each month for the next 12 years. Find the monthly amount. (a) Decide whether the problem relates to an ordinary annuity or an annuity due, and then (b) Solve the problem.
A 10-year Emmaco Corporate bond has a par value of $10,000 with coupons at 7.8% paid semiannually.(a) If this bond is bought to yield 10% compounded semiannually, find its price.(b) Suppose that after this bond has been held for 2 years, the desired yield is 8% compounded semiannually. Find the
Kodicom, Inc. has 15-year bonds with a $5000 maturity value and a quoted coupon rate of 12% paid semiannually. The current yield is 10% compounded semiannually.(a) Compute the price of these bonds.(b) Suppose that with 12 years remaining until maturity, the yield rate drops to 8% compounded
Suppose an individual makes an initial investment of $2500 in an account that earns 7.8%, compounded monthly, and makes additional contributions of $100 at the end of each month for a period of 12 years. After these 12 years, this individual wants to make withdrawals at the end of each month for
Suppose that Nam Banh deposits his $12,500 bonus in an account that earns 8%, compounded quarterly, and makes additional deposits of $500 at the end of each quarter for the next 2212years, until he retires. To supplement his retirement, Nam wants to make withdrawals at the end of each quarter for
A young couple wants to have a college fund that will pay $30,000 at the end of each half-year for 8 years.(a) If they can invest at 8%, compounded semiannually, how much do they need to invest at the end of each 6-month period for the next 18 years in order to begin making their college
A recent college graduate begins a savings plan at age 27 by investing $400 at the end of each month in an account that earns 7.5%, compounded monthly.(a) If this plan is followed for 10 years, how much should the monthly contributions be for the next 28 years in order to be able to withdraw
Find the present value of an annuity of $2000, at the end of each quarter for 5 years after being deferred for 3 years, if money is worth 8% compounded quarterly.
Find the present value of an annuity of $2000 per year at the end of each of 8 years after being deferred for 6 years, if money is worth 7% compounded annually?
The terms of a single parent's will indicate that a child will receive an ordinary annuity of $16,000 per year from age 18 to age 24 (so the child can attend college) and that the balance of the estate goes to a niece. If the parent dies on the child's 14th birthday, how much money must be removed
1. Find the present value of an annuity of $6000 paid at the end of each 6-month period for 8 years if the interest rate is 8%, compounded semiannually? 2. Find the present value of an annuity that pays $3000 at the end of each 6-month period for 6 years if the interest rate is 6%, compounded
On his 48th birthday, a man wants to set aside enough money to provide an income of $1500 at the end of each month from his 60th birthday to his 65th birthday. If he earns 6%, compounded monthly, how much will this supplemental retirement plan cost him on his 48th birthday?
The semiannual tuition payment at a major university is expected to be $30,000 for the 4 years beginning 18 years from now. What lump sum payment should the university accept now, in lieu of tuition payments beginning 18 years, 6 months from now? Assume that money is worth 7%, compounded
A community is soliciting pledges for a fitness center building project to begin in 3 years. If money is worth 6%, compounded quarterly, how much must a family deposit now in order to contribute $2500 at the end of each quarter for 2 ½ year after the project begins?
Danny Metzger's parents invested $1600 when he was born. This money is to be used for Danny's college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19. Find the amount that will be available each year, if money is worth 6%, compounded annually.
Carol Goldsmith received a trust fund inheritance of $10,000 on her 30th birthday. She plans to use the money to supplement her income with 20 quarterly payments beginning on her 60th birthday. If money is worth 7.6% compounded quarterly, how much will each quarterly payment be?
The May 18, 2013, Powerball, worth $590.5 million and won by an 84-year-old resident of Zephyrillis, Florida, was the largest individual jackpot ever. (Note that in March 2012 three ticket holders split the largest-ever Powerball prize of $656 million.) Rather than take the prize in 30 annual
A couple received a $134,000 inheritance the year they turned 48 and invested it in a fund that earns 7.7% compounded semiannually. If this amount is deferred for 14 years (until they retire), how much will it provide at the end of each half-year for the next 20 years after they retire?
Suppose a couple have $100,000 at retirement that they can invest in an ordinary annuity that earns 7.8%, compounded monthly. Track the balance in this annuity account until it reaches $0, if the couple receives the following monthly payments. (a) $1000 (b) $2500
Suppose you invested $250,000 in an annuity that earned interest compounded monthly. This annuity paid $3000 at the end of each month. Experiment with the following different interest rates (compounded monthly) to see how long it will be, with each rate, until this annuity has an account balance of
1. Suppose a state lottery prize of $5 million is to be paid in 20 payments of $250,000 each at the end of each of the next 20 years. If money is worth 10%, compounded annually, what is the present value of the prize? 2. How much is needed in an account that earns 8.4% compounded monthly in order
1. With a present value of $135,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 6.4%, compounded quarterly? 2. If $88,000 is invested in an annuity that earns 5.8%, compounded quarterly, what payments will it provide at
Two loans are for the same amount at the same interest rate; one is paid off in 10 years and the other in 25 years. (a) Which loan results in more of each payment being directed toward principal? Explain. (b) Which loan results in a lower periodic payment? Explain.
A $10,000 loan is to be amortized for 10 years with quarterly payments of $334.27. If the interest rate is 6%, compounded quarterly, what is the unpaid balance immediately after the sixth payment?
A debt of $8000 is to be amortized with 8 equal semiannual payments of $1288.29. If the interest rate is 12%, compounded semiannually, find the unpaid balance immediately after the fifth payment.
When Maria Acosta bought a car 212 years ago, she borrowed $28,000 for 48 months at 8.1% compounded monthly. Her monthly payments are $684.88, but she'd like to pay off the loan early. How much will she owe just after her payment at the 212 -year mark?
Six-and-a-half years ago, a small business borrowed $50,000 for 10 years at 9%, compounded semiannually, in order to update some equipment. Now the company would like to pay off this loan. Find the payoff amount just after the company makes the 14th semiannual payment of $3843.81?
A man buys a house for $350,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 10 years. The interest rate on the debt is 12%, compounded semiannually.(a) The size of each payment.(b) The total amount paid for each purchase.(c)
Sean Lee purchases $20,000 worth of supplies for his restaurant by making a $3000 down payment and amortizing the remaining cost with quarterly payments over the next 5 years. The interest rate on the debt is 16%, compounded quarterly. (a) The size of each payment. (b) The total amount paid for
A woman buys an apartment house for $1,250,000 by making a down payment of $250,000 and amortizing the rest of the purchase price with monthly payments over the next 10 years. The interest rate on the debt is 7.2%, compounded monthly. (a) The size of each payment. (b) The total amount paid for each
1. When a debt is amortized, which interest rate is better for the borrower, 10% or 6%? Explain. 2. A debt of $8000 is to be amortized with 8 equal semiannual payments. If the interest rate is 12%, compounded semiannually, what is the size of each payment?
John Fare purchased $10,000 worth of equipment by making a $2000 down payment and promising to pay the remainder of the cost in semiannual payments over the next 4 years. The interest rate on the debt is 10%, compounded semiannually? (a) The size of each payment. (b) The total amount paid for each
1. A man buys a car for $36,000. If the interest rate on the loan is 12%, compounded monthly, and if he wants to make monthly payments of $900 for 36 months, how much must he put down? 2. A woman buys a car for $40,000. If the interest rate on the loan is 12%, compounded monthly, and if she wants
A couple purchasing a home budget $1800 per month for their loan payment. If they have $20,000 available for a down payment and are considering a 25-year loan, how much can they spend on the home at each of the following rates? (a) 6.9% compounded monthly (b) 7.5% compounded monthly
A developer wants to buy a certain parcel of land. The developer feels she can afford payments of $44,000 each half-year for the next 7 years. How much can she borrow and hold to this budget at each of the following interest rates? (a) 8.9% compounded semiannually (b) 7.3% compounded semiannually
A couple who borrow $90,000 for 30 years at 7.2%, compounded monthly, must make monthly payments of $610.91. (a) Find their unpaid balance after 1 year. (b) During that first year, how much interest do they pay?
A company that purchases a piece of equipment by borrowing $250,000 for 10 years at 6%, compounded monthly, has monthly payments of $2775.51.(a) Find the unpaid balance on this loan after 1 year.(b) During that first year, how much interest does the company pay?
When Otto and Millie bought their home, they borrowed $200,000 for 30 years at 6% compounded monthly. After making 120 payments of $1199.10, they plan to refinance at 4.5% compounded monthly for 15 years, with refinancing costs of $750 added to the amount of the new loan. (a) Find the amount of the
In order to upgrade its equipment, Simon Reilly Chemicals (SRC) borrowed $2.8 million at 6.4% compounded quarterly for 20 years. After making 18 quarterly payments of $62,297.39, SRC plans to refinance this loan at 5.2% compounded quarterly for 10 years, with refinancing charges of $12,000 added to
A recent college graduate buys a new car by borrowing $18,000 at 8.4%, compounded monthly, for 5 years. She decides to pay an extra $15 per payment. (a) What is the monthly payment required by the loan, and how much does she decide to pay each month? (b) How many payments (that include the extra
A young couple buying their first home borrow $85,000 for 30 years at 7.2%, compounded monthly, and make payments of $576.97. After 3 years, they are able to make a one-time payment of $2000 along with their 36th payment.(a) Find the unpaid balance immediately after they pay the extra $2000 and
Jadele, Inc., borrowed $12.8 million at 7.2% compounded quarterly for 30 years for construction of a new manufacturing facility. After making 42 quarterly payments of $261,094.80, it plans to refinance the existing loan for an amount that includes an additional $1.1 million for expansion. Jadele
When Gustavo and Serrana bought their home, they had a 5.7% loan with monthly payments of $870.60 for 30 years. After making 78 monthly payments, they plan to refinance for an amount that includes an additional $35,000 to remodel their kitchen. They can refinance at 4.8% compounded monthly for 25
A debt of $100,000 is amortized at 6%, compounded monthly, over 25 years with 300 monthly payments of $644.30 each. The following figure includes two graphs: One shows the total amount paid (in monthly payments) as a function of time (in months), and the other shows the amount paid toward the
A debt of $100,000 is amortized at 6%, compounded monthly, over 25 years with 300 monthly payments of $644.30 each. The following figure includes two graphs: One shows the total amount paid (in monthly payments) as a function of time (in months), and the other shows the amount paid toward the
What difference does 0.5% make on a loan? To answer this question, find (to the nearest dollar) the monthly payment and total interest paid over the life of the loan for each of the following.(a) An auto loan of $15,000 at 8.0% versus 8.5%, compounded monthly, for 4 years.(b) A mortgage loan of
Some banks now have biweekly mortgages (that is, with payments every other week). Compare a 20-year, $100,000 loan at 8.1% by finding the payment size and the total interest paid over the life of the loan under each of the following conditions. (a) Payments are monthly, and the rate is 8.1%,
Many banks charge points on mortgage loans. Each point is the equivalent of a 1% charge on the amount borrowed and is paid before the loan is made as part of the closing costs of buying a home (closing costs include points, title fees, attorney's fees, assessor's fees, and so on). (a) If $100,000
Time-share sales provide an opportunity for vacationers to own a resort condo for 1 week (or more) each year forever. The owners may use their week at their own condo or trade the week and vacation elsewhere.Time-share vacation sales usually require payment in full or financing through the
During four years of college, Nolan MacGregor's student loans are $4000, $3500, $4400, and $5000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1%, compounded quarterly, while Nolan is in school and 3%, compounded quarterly, during a 6-month grace period
1. A loan of $10,000 is to be amortized with 10 equal quarterly payments. If the interest rate is 6%, compounded quarterly, what is the periodic payment? 2. A recent graduate's student loans total $18,000. If these loans are at 4.2%, compounded quarterly, for 10 years, what are the quarterly
Clark and Lana take a 30-year home mortgage of $121,000 at 7.8%, compounded monthly. They make their regular monthly payments for 5 years, then decide to pay $1000 per month.(a) Find their regular monthly payment.(b) Find the unpaid balance when they begin paying the $1000.(c) How many payments of
Develop an amortization schedule for a 4-year car loan if $16,700 is borrowed at 8.2%, compounded monthly.
Develop an amortization schedule for a 10-year mortgage loan of $80,000 at 7.2%, compounded monthly?
For equipment upgrades a business borrowed $400,000 at 8%, compounded semiannually, for 5 years. What are the semiannual payments?
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