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mathematics
calculus

Questions and Answers of Calculus

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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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%
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%,
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
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
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
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
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
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
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
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
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
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%,
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
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%,
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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?
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
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
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%,
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
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
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%,
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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%,
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
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
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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