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mathematics
calculus

Questions and Answers of Calculus

Mrs. Gonzalez lent $2500 to her son Luis for 7 months at 9% annual simple interest. What is the future value of this loan?
A couple bought some stock for $30 per share that pays an annual dividend of $0.90 per share. After 1 year the price of the stock was $33. Find the simple interest rate on the growth of their
1. Jenny Reed bought SSX stock for $16 per share. The annual dividend was $1.50 per share, and after 1 year SSX was selling for $35 per share. Find the simple interest rate of growth of her money?2.
Janie Christopher lent $6000 to a friend for 90 days at 12%. After 30 days, she sold the note to a third party for $6000. What annual simple interest rate did the third party receive? Use 360 days in
A firm buys 12 file cabinets at $140 each, with the bill due in 90 days. How much must the firm deposit now to have enough to pay the bill if money is worth 12% simple interest per year? Use 360 days
A student has a savings account earning 9% simple interest. She must pay $1500 for first-semester tuition by September 1 and $1500 for second-semester tuition by January 1. How much must she earn in
If you want to earn 15% annual simple interest on an investment, how much should you pay for a note that will be worth $13,500 in 10 months?
What is the present value of an investment at 6% annual simple interest if it is worth $832 in 8 months?
If $5000 is invested at 8% annual simple interest, how long does it take to be worth $9000?
How long does it take for $8500 invested at 11% annual simple interest to be worth $13,000?
A retailer owes a wholesaler $500,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. The retailer can get a 45-day certificate of deposit (CD) paying 6% or a 60-day
An investor owns several apartment buildings. The taxes on these buildings total $30,000 per year and are due before April 1. The late fee is 1 2% per month up to 6 months, at which time the
Bill Casler bought a $2000, 9-month certificate of deposit (CD) that would earn 8% annual simple interest. Three months before the CD was due to mature, Bill needed his CD money, so a friend agreed
Suppose you lent $5000 to friend 1 for 18 months at an annual simple interest rate of 9%. After 1 year you need money for an emergency and decide to sell the note to friend 2. (a) How much does
Write the first ten terms of the sequence defined by an = 3n.
Write the first seven terms of the sequence defined by an = 2/n.
1. Write the first six terms of the sequence whose nth term is (-1)n /(2n + 1)? 2. Write the first five terms of the sequence whose nth term is an = (-1)n/ (n2)?
1. Write the first four terms and the 10th term of the sequence whose nth term is2. Write the sixth term of the sequence whose nth term is
(a) Identify d and a1 and (b) write the next three terms.1. 2, 5, 8, ...2. 3, 9, 15, ...3. 3, 9/2, 6,...4. 2, 2.75, 3.5, . . .
1. Find the 83rd term of the arithmetic sequence with first term 6 and common difference - ½? 2. Find the 66th term of the arithmetic sequence with first term 12 and common difference -1/3?
1. Find the 100th term of the arithmetic sequence with first term 5 and eighth term 19? 2. Find the 73rd term of the arithmetic sequence with first term 20 and 10th term 47?
1. Find the sum of the first 38 terms of the arithmetic sequence with first term 2 and 38th term 113? 2. Find the sum of the first 56 terms of the arithmetic sequence with first term 6 and 56th term
Find the sum of the first 70 terms of the arithmetic sequence with first term 10 and common difference ½?
Find the sum of the first 80 terms of the arithmetic sequence with first term 12 and common difference - 3?
Find the sum of the first 150 terms of the arithmetic sequence 6, 9/2, 3, . . . ?
Find the sum of the first 200 terms of the arithmetic sequence 12, 9, 6, . . . .?
1. Bee reproduction A female bee hatches from a fertilized egg, whereas a male bee hatches from an unfertilized egg. Thus a female bee has a male parent and a female parent, but a male bee has only a
1. A new firm loses $4000 in its first month, but its profit increases by $800 in each succeeding month for the next year. What is its profit in the 12th month? 2. If you make $36,000 and get $2400
$10,000 is invested for 6 years at an annual simple interest rate of 16%. (a) How much interest will be earned? (b) What is the future value of the investment at the end of the 6 years?
Suppose you are offered two identical jobs: one paying a starting salary of $40,000 with yearly raises of $2000 and one paying a starting salary of $36,000 with yearly raises of $2400. Which job will
1. A new firm loses $4000 in its first month, but its profit increases by $800 in each succeeding month for the next year. What is its profit for the year?2. Pay raises If you are an employee, would
As an employee, would you prefer being given a $2400 raise each year for 5 years or a $400 raise each quarter for 5 years?
$800 is invested for 5 years at an annual simple interest rate of 14%. (a) How much interest will be earned? (b) What is the future value of the investment at the end of the 5 years?
$1000 is invested for 3 months at an annual simple interest rate of 12%. (a) How much interest will be earned? (b) What is the future value of the investment after 3 months?
$1800 is invested for 9 months at an annual simple interest rate of 15%. (a) How much interest will be earned? (b) What is the future value of the investment after 9 months?
If you borrow $800 for 6 months at 16% annual simple interest, how much must you repay at the end of the 6 months?
Find the requested value and identify each of the other values as the periodic rate, the number of periods, the principal, or the future value.1. Find S: S = 2000(1 + 0.02)242. Find S: S = 15,000(1 +
1. What are the future value and the interest earned if $3200 is invested for 5 years at 8% compounded quarterly? 2. What interest will be earned if $6300 is invested for 3 years at 12% compounded
1. What lump sum do parents need to deposit in an account earning 10%, compounded monthly, so that it will grow to $80,000 for their son's college fund in 18 years?2. What lump sum should be
1. What present value amounts to $10,000 if it is invested for 10 years at 6% compounded annually? 2. What present value amounts to $300,000 if it is invested at 7%, compounded semiannually, for 15
1. Find the future value if $5100 is invested for 4 years at 9% compounded continuously? 2. Find the interest that will result if $8000 is invested at 7%, compounded continuously, for 8 years?
1. What is the compound interest if $410 is invested for 10 years at 8% compounded continuously?2. If $8000 is invested at 8.5% compounded continuously, find the future value after 412 years?
Grandparents want to make a gift of $100,000 for their grandchild's 20th birthday. How much would have to be invested on the day of their grandchild's birth if their investment could earn (a) 10.5%
Suppose an individual wants to have $200,000 available for her child's education. Find the amount that would have to be invested at 12%, compounded continuously, if the number of years until college
Which investment will earn more money, a $1000 investment for 5 years at 8% compounded annually or a $1000 investment for 5 years compounded continuously at 7%?
How much more interest will be earned if $5000 is invested for 6 years at 7% compounded continuously, instead of at 7% compounded quarterly?
Find the annual percentage yield for an investment at (a) 7.3% compounded monthly (b) 6% compounded continuously.
What is the annual percentage yield (or effective annual rate) for a nominal rate of (a) 8.4% compounded quarterly and (b) 10% compounded continuously?
Rank each interest rate and compounding scheme in order from highest yield to lowest yield.1. 8% compounded quarterly, 8% compounded monthly, 8% compounded annually?2. 6% compounded continuously, 6%
Two different investment companies offer college savings plans, one at 8.2% compounded continuously and the other at 8.4% compounded quarterly. Which is the better investment?
1. For life insurance policies, some of the premium pays for the cost of the insurance, and the remainder goes toward the cash value of the policy and earns interest like a savings account. Suppose
The figure shows a graph of the future value of $350 at 6% compounded monthly, along with the graph of $350 at 6% compounded annually. Which is which?Explain.
Microsoft's stock price peaked at 6118% of its I.P.O. price more than 13 years after the I.P.O. (Source: Bloomberg Financial Markets). Suppose that $10,000 invested in Microsoft at its I.P.O. price
If $10,000 had been invested in the Saga more Capital Opportunity Fund on September 30, 2004, it would have been worth $46,649.55 on September 30, 2014. What interest rate, compounded annually, did
How long (in years) would $700 have to be invested at 11.9%, compounded continuously, to earn $300 interest?
How long (in years) would $600 have to be invested at 8%, compounded continuously, to amount to $970?
At what nominal rate, compounded quarterly, would $20,000 have to be invested to amount to $26,425.82 in 7 years?
At what nominal rate, compounded annually, would $10,000 have to be invested to amount to $14,071 in 7 years?
1. For her 1st birthday, Ruth's grandparents invested $1000 in an 18-year certificate for her that pays 8% compounded annually. How much will the certificate be worth on Ruth's 19th birthday?2. To
(a) A 40-year-old man has $432,860 in an IRA account. He decides to make no additional contributions to the account but expects it to grow at 7.5% compounded annually. How much does he expect to have
(a) The purchase of Alaska cost the United States $7 million in 1869. If this money had been placed in a savings account paying 6% compounded annually, how much money would be available from this
A couple needs $45,000 as a down payment for a home. If they invest the $30,000 they have at 8% compounded quarterly, how long will it take for the money to grow into $45,000?
How long does it take for an account containing $8000 to be worth $15,000 if the money is invested at 9% compounded monthly?
Mary Stahley invested $2500 in a 36-month certificate of deposit (CD) that earned 8.5% annual simple interest. When the CD matured, she invested the full amount in a mutual fund that had an annual
Suppose Patrick Goldsmith deposited $1000 in an account that earned simple interest at an annual rate of 7% and left it there for 4 years. At the end of the 4 years, Patrick deposited the entire
Use a spreadsheet or financial program on a calculator or computer.1. Track the future values of two investments of $5000, one at 6.3% compounded quarterly and another at 6.3% compounded monthly for
For each geometric sequence given in Problems 1 and 2, write the next three terms.1. (a) 3, 6, 12, . . .(b) 81, 54, 36, . . .2. (a) 4, 12, 36, . . .(b) 32, 40, 50, . . .
Identify (a) the annual interest rate, (b) the length of the investment in years, (c) the periodic interest rate, and (d) the number of periods of the investment.1. 8% compounded quarterly for 7
Write an expression that gives the requested term or sum.1. The 13th term of the geometric sequence with first term 10 and common ratio 22. The 11th term of the geometric sequence with first term 6
1. A house that 20 years ago was worth $160,000 has increased in value by 4% each year because of inflation. What is its worth today?2. If inflation causes the cost of automobiles to increase by 3%
Population growth Suppose a country has a population of 20 million and projects a growth rate of 2% per year for the next 20 years. What will the population of this country be in 10 years?
1. Spread of AIDS Suppose a country is so devastated by the AIDS epidemic that its population decreases by 0.5% each year for a 4-year period. If the population was originally 10 million, what is the
Population If a population of 8 million begins to increase at a rate of 0.1% each month, in how many months will it be 10 million?
A ball is dropped from a height of 128 feet. If it rebounds ¾ of the height from which it falls every time it hits the ground, how high will it bounce after it strikes the ground for the fourth time?
1. A pump removes 13 of the water in a container with every stroke. What amount of water is still in a container after 5 strokes if it originally contained 81 cm3?2. A machine is valued at $10,000.
1. Suppose a new business makes a $1000 profit in its first month and has its profit increase by 10% each month for the next 2 years. How much profit will the business earn in its 12th month?2. The
1. Bacterial growth If a bacteria culture increases by 20% every hour and 2000 are present initially, how many will be present at the end of 10 hours?2. Profit If changing market conditions cause a
1. Suppose a new business makes a $1000 profit in its first month and has its profit increase by 10% each month for the next 2 years. How much profit will it earn in its first year?2. Suppose you
1. Mailing chain letters that involve sending money has been declared illegal because most people would receive nothing while a comparative few would profit. Suppose the chain letter in Problem 75
1. Find the future value if $8000 is invested for 10 years at 12% compounded annually?2. What is the future value if $8600 is invested for 8 years at 10% compounded semiannually?
1. Find S: S = 25002. Find S: S = 10003. Find R: S = 80,0004. Find R: S = 25,000
1. The Weidmans want to save $40,000 in 2 years for a down payment on a house. If they make monthly deposits in an account paying 12%, compounded monthly, what is the size of the payments that are
If $2500 is deposited at the end of each quarter in an account that earns 5% compounded quarterly, after how many quarters will the account contain $80,000?
If $4000 is deposited at the end of each half year in an account that earns 6.2% compounded semiannually, how long will it be before the account contains $120,000?
In this section's Application Preview, we considered the investment strategies of twins and found that starting early and stopping was a significantly better strategy than waiting, in terms of total
(a) Patty Stacey deposits $2000 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end
1. Find the future value of an annuity due of $100 each quarter for 21/2 years at 12%, compounded quarterly? 2. Find the future value of an annuity due of $1500 each month for 3 years if the
1. Find the future value of an annuity due of $200 paid at the beginning of each 6-month period for 8 years if the interest rate is 6%, compounded semiannually? 2. A house is rented for $3600 per
1. How much must be deposited at the beginning of each year in an account that pays 8%, compounded annually, so that the account will contain $24,000 at the end of 5 years? 2. What is the size of the
A company wants to have $800,000 for office renovations. If it can deposit $40,000 at the beginning of each quarter into an account that earns 5.2% compounded quarterly, how long before the company
Seana wants to save $20,000 toward a new car purchase. She can contribute $400 at the beginning of each month into an account that earns 4.8% compounded monthly. How long until the account reaches
Parents agree to invest $500 (at 10%, compounded semiannually) for their son on the December 31 or June 30 following each semester that he makes the dean's list during his 4 years in college. If he
Jake Werkheiser decides to invest $2000 in an IRA at the end of each year for the next 10 years. If he makes these investments, and if the certificates pay 12%, compounded annually, how much will he
How much will have to be invested at the beginning of each year at 10%, compounded annually, to pay off a debt of $50,000 in 8 years? (a) State whether the problem relates to an ordinary annuity or
If $1000 is deposited at the beginning of each quarter into an account that earns 8%, compounded quarterly, how long until the account contains $31,000? (a) State whether the problem relates to an
A family wants to have a $200,000 college fund for their children at the end of 20 years. What contribution must be made at the end of each quarter if their investment pays 7.6%, compounded
If $2000 is deposited at the end of each quarter into an account that earns 6% compounded quarterly, how long until the account reaches $50,000? (a) State whether the problem relates to an ordinary
A couple has determined that they need $1.5 million to establish an annuity when they retire in 25 years. How much money should they deposit at the end of each month in an investment plan that pays
Sam deposits $500 at the end of every 6 months in an account that pays 8%, compounded semiannually. How much will he have at the end of 8 years? (a) State whether the problem relates to an ordinary
A company deposits $12,000 at the beginning of each quarter into an account that earns 7.2% compounded quarterly. How much will be in this account after 5 years? (a) State whether the problem

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