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College Mathematics for Business Economics Life Sciences and Social Sciences 12th edition Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen - Solutions
What is the purchase price of a 26-week T-bill with a maturity value of $1,000 that earns an annual interest rate of 4.903%?
To complete the sale of a house, the seller accepts a 180-day note for $10,000 at 7% simple interest. (Both interest and principal are repaid at the end of 180 days.) Wishing to use the money sooner for the purchase of another house, the seller sells the note to a third party for $10,124 after 60
An investor purchases 450 shares at $21.40 a share, holds the stock for 26 weeks, and then sells the stock for $24.60 a share.Use the commission schedule from Company B shown in Table 3 to find the annual rate of interest earned by each investment in Problems 61 and 62.
An investor purchases 75 shares at $37.90 a share, holds the stock for 150 days, and then sells the stock for $41.20 a share.Many tax preparation firms offer their clients a refund anticipation loan (RAL). For a fee, the firm will give a client his refund when the return is filed. The loan is
A client receives a $1,100 RAL, which is paid back in 30 days.
A client receives a $3,000 RAL, which is paid back in 25 days.
In Problem, use the continuous compound interest formula (2) to find each of the indicated values. A = $32,982; P = $27,200; t = 5.93% ; t = ?
In Problem, use the continuous compound interest formula (2) to find each of the indicated values. A = $23,600; P = $19,150; t = 60months ; = ?
In Problem, use compound interest formula (1) to find each of the indicated values. P = $2,800; I = 0.003; n = 24; A = ?
If $2,000 is invested at 7% compounded (A) annually (B) quarterly (C) monthly what is the amount after 5 years? How much interest is earned?
If $20,000 is invested at 4% compounded monthly, what is the amount after (A) 5 years? (B) 8 years?
If $23,000 is invested at 13.5% compounded continuously, what is the amount after 15 years?
Discuss the similarities and differences in the graphs of future value A as a function of time t for loans of $4,000, $8,000, and $12,000, respectively, each at 7.5% compounded monthly for 8 years (see the figure).
If $2,000 is invested in an account that earns 8.25% compounded annually for 5 years, find the interest earned during each year and the amount in the account at the end of each year. Organize your results in a table.
If an investment company pays 8% compounded quarterly, how much should you deposit now to have $6,000 (A) 3 years from now? (B) 6 years from now?
If an investment earns 12% compounded continuously, how much should you deposit now to have $4,800 (A) 48 months from now? (B) 7 years from now?
In Problem use compound interest formula (1) to find each of the indicated values. A = $15,000; I = 0.01; n = 28; P = ?
What is the annual percentage yield (APY) for money invested at an annual rate of (A) 4.32% compounded monthly? (B) 4.31% compounded daily?
What is the annual percentage yield (APY) for money invested at an annual rate of (A) 3.05% compounded quarterly? (B) 2.95% compounded continuously?
How long will it take $5,000 to grow to $7,000 if it is invested at 6% compounded quarterly?
How long will it take $42,000 to grow to $60,276 if it is invested at 4.25% compounded continuously?
A = 2P; i = 0.05; n = ? use the compound interest formula (I) to find n to the nearest larger integer value.
How long will it take money to double if it is invested at (A) 8% compounded semiannually? (B) 7% compounded semiannually?
How long will it take money to double if it is invested at (A) 21% compounded continuously? (B) 33% compounded continuously?
A person with $14,000 is trying to decide whether to purchase a car now, or to invest the money at 6.5% compounded semiannually and then buy a more expensive car. How much will be available for the purchase of a car at the end of 3 years?
If the inflation rate averages 4% per year compounded annually for the next 5 years, what will a car that costs $17,000 now cost 5 years from now?
In a suburb, housing costs have been increasing at 5.2% per year compounded annually for the past 8 years. A house worth $260,000 now would have had what value 8 years ago?
In Problem, use the continuous compound interest formula (2) to find each of the indicated values. A = $995; r = 22 %; t = 2 years; A = ?
If the world population is now about 6.5 billion people and is growing at 1.14% compounded continuously, how long will it take the population to grow to 10 billion people? (Round up to the next-higher year if not exact.)
Which is the better investment and why: 8% compounded quarterly or 8.3% compounded annually?
(A) Starting with formula (1). derive each of the following formulas:(B) Explain why it is unnecessary to memorize the formulas above for P, i, and n if you know formula (1).
If you deposit $10,000 in a savings account now, what rate compounded continuously would be required for you to withdraw $12,500 at the end of 4 years?
A married couple has $15,000 toward the purchase of a house. For the house that the couple wants to buy, a down payment of $20,000 is required. How long will the money have to be invested at 7% compounded quarterly to grow to $20,000? (Round up to the next-higher quarter if not exact.)
If $1 had been placed in a bank account in the year 1066 and forgotten until now, how much would be in the account at the end of 2016 if the money earned 2% interest compounded annually? 2% simple interest? (Now you can see the power of compounding and why inactive accounts are closed after a
How long will it take money to triple if it is invested at 5% compounded daily? 6% compounded continuously?
Refer to Problem 73. Show that the exact annual compound rate of growth of an investment that doubles in n years is given by r = 100(21/n - 1). Graph this equation and the rule of 72 on a graphing calculator for 5 ≤ n ≤ 20.
How long does it take for a $4,800 investment at 8% compounded monthly to be worth more than a $5,000 investment at 5% compounded monthly? Solve Problem using graphical approximation techniques on a graphing calculator.
One investment pays 9% simple interest and another pays 6% compounded monthly. Which investment would you choose? Why? Solve Problem using graphical approximation techniques on a graphing calculator.
In Problem, use the continuous compound interest formula (2) to find each of the indicated values. A = $19,000; r = $7.69%; t = 5 years; P = ?
What is the annual nominal rate compounded monthly for a CD that has an annual percentage yield of 5.9%?
What annual nominal rate compounded continuously has the same annual percentage yield as 6% compounded monthly?
A zero coupon bond with a face value of $20,000 matures in 10 years. What should the bond be sold for now if its rate of return is to be 4.194% compounded annually? Refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in
If you pay $32,000 for a 5-year zero coupon bond with a face value of $40,000, what is your annual compound rate of return? Refer to zero coupon bonds. A zero coupon bond is a bond that is sold now at a discount and will pay its face value at some time in the future when it matures no interest
An online financial service listed the following 1-year CD accounts: (A) Banking for CDs: 4.5% compounded quarterly (B) Wingspan Bank: 4.6% compounded monthly (C) Discover Bank: 4.6% compounded continuously What is the annual percentage yield (to three decimal places) of each?
The buying and selling commission schedule shown at the top of the next column is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in problemFind the annual
The buying and selling commission schedule shown at the top of the next column is from an online discount brokerage firm. Taking into consideration the buying and selling commissions in this schedule, find the annual compound rate of interest earned by each investment in problemFind the annual
In Problem, use the future value formula (6) to find each of the indicated values. n = 25; i = 0.04; PMT = $100; FV = ?
In Problem, use the future value formula (6) to find each of the indicated values. FV = $2,500; n = 10; i = 0.08; PMT = ?
In Problem, use the future value formula (6) to find each of the indicated values FV = $8,000; i = 0.04; PMT = 500; n = ?
In Problem, use the future value formula (6) to find each of the indicated values FV = $4,100; PMT = $100; n = 20; I = ? (Round answer to two decimal places.)
Explain why no interest is credited to an ordinary annuity at the end of the first period.
Monthly deposits of $350 are made for 6 years into an annuity that pays 6% compounded monthly In Problem, find i (the rate per period) and n (the number of periods) for each annuity.
Solve the future value formula (6) for I if n =2.
USG Annuity and Life offered an annuity that pays 7.25% compounded monthly. If $1,000 is deposited into this annuity every month, how much is in the account after 15 years? How much of this is interest?
A self-employed person has a Keogh retirement plan. (This type of plan is free of taxes until money is withdrawn.) If deposits of $7,500 are made each year into an account paying 8% compounded annually, how much will be in the account after 20 years?
Recently, The Hartford offered an annuity that pays 5.5% compounded monthly. What equal monthly deposit should be made into this annuity in order to have $100,000 in 10 years?
Parents have set up a sinking fund in order to have $120,000 in 15 years for their children's college education. How much should be paid semiannually into an account paying 6.8% compounded semiannually?
If $2.(XK) is deposited at the end of each quarter for 2 years into an ordinary annuity earning 7.9% compounded quarterly, construct a balance sheet showing the interest earned during each quarter and the balance at the end of each quarter.
If $500 is deposited each quarter into an account paying 8% compounded quarterly for 3 years, find the interest earned during each of the 3 years.
John procrastinates and does not make his first $1,000 deposit into an IRA until he is 36, but then he continues to deposit $1,000 each year until he is 65 (30 deposits in all). If John's IRA also earns 6.4% compounded annually, how much is in his IRA when he makes his last deposit on his 65th
Suppose that Bob decides to continue to make $1,000 deposits into his IRA every year until his 65th birthday. If John still waits until he is 36 to start his IRA, how much must he deposit each year in order to have the same amount at age 65 as Bob has? For Information: Problems 33 and 34.
American Express's online banking division offered a money market account with an APY of 5.65%. (A) If interest is compounded monthly, what is the equivalent annual nominal rate? (B) If a company wishes to have $1,000,000 in this account after 8 years, what equal deposit should be made each month?
A company establishes a sinking fund for upgrading office equipment with monthly payments of $2,000 into an account paying 6.6% compounded monthly. How long will it be before the account has $100,000? (Round up to the next-higher month if not exact.)
A person invests $2,000 annually in an IRA. At the end of 6 years, the amount in the fund is $14,000. What annual nominal compounding rate has this fund earned? In Problem, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as
At the end of each month, an employee deposits $80 into a credit union account. At the end of 2 years, the account contains $2,100. What annual nominal rate compounded monthly has this account earned? In Problem, use graphical approximation techniques or an equation solver to approximate the
When would an ordinary annuity consisting of monthly payments of $200 at 5% compounded monthly be worth more than a principal of $10,000 invested at 7.5% compounded monthly? In Problem, use graphical approximation techniques to answer the question.
Semiannual deposits of $1,900 are made for 7 years into an annuity that pays 8.5% compounded semiannually. In Problem, find i (the rate per period) and n (the number of periods) for each annuity.
Quarterly deposits of $1,200 are made for 18 years into an annuity that pays 7.6% compounded quarterly. In Problem find i (the rate per period) and n (the number of periods) for each annuity.
In problem, use formula (5) or (6) to solve each problem. PV = $20,000; I = 0.0175; PMT = $500; n = ?
In problem, use formula (5) or (6) to solve each problem. PV = $12,000; PMT = $400; n = 40; / = ? (Round answer to three decimal places.)
Solve the present value formula (5) for n. In Problem, use formula (5) or (6) to solve problem.
Semiannual payments of $3,200 are made for 12 years to repay a loan at 9.9% compounded semiannually. In Problems, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate.
Explain why the last payment in an amortization schedule might differ from the other payments. In Problem, use formula (5) or (6) to solve problem.
American General offers a 7-year ordinary annuity with a guaranteed rate of 6.35% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $10,000 annually over the 7-year period?
E-Loan recently offered 36-month auto loans at 9.84% compounded monthly to applicants with fair credit ratings. If you have a fair credit rating and can afford monthly payments of $350, how much can you borrow from E-Loan? What is the total interest you will pay for this loan?
If you buy a computer directly from the manufacturer for $3,500 and agree to repay it in 60 equal installments at 1.75% interest per month on the unpaid balance, how much are your monthly payments? How much total interest will be paid?
Use the information given in the Bison wagon ad to determine if this is really 0% financing. If not, explain why and determine what rate a consumer would be charged for financing one of these wagons.
You want to purchase an automobile for $28,500. The dealer offers you 0% financing for 60 months or a $6,000 rebate. You can obtain 6.2% financing for 60 months at the local bank. Which option should you choose? Explain.
A recreational vehicle costs $80,000. You pay 10% down and amortize the rest with equal monthly payments over a 7-year period. If you pay 9.25% compounded monthly, what is your monthly payment? How much interest will you pay?
Construct the amortization schedule for a $10,000 debt that is to be amortized in six equal quarterly payments at 2.6% interest per quarter on the unpaid balance.
A man establishes an annuity for retirement by depositing $50,000 into an account that pays 7.2% compounded monthly. Equal monthly withdrawals will be made each month for 5 years, at which time the account will have a zero balance. Each year taxes must be paid on the interest earned by the account
A family is thinking about buying a new house costing $120,000. The family must pay 20% down, and the rest is to be amortized over 30 years in equal monthly payments. If money costs 7.5% compounded monthly, what will the monthly payment be? How much total interest will be paid over 30 years?
Annual payments of $1,045 are made for 5 years to repay a loan at 4.75% compounded annually. In Problems, find i (the rate per period) and n (the number of periods) for each loan at the given annual rate.
A person establishes a sinking fund for retirement by contributing $7,500 per year at the end of each year for 20 years. For the next 20 years, equal yearly payments are withdrawn, at the end of which time the account will have a zero balance. If money is worth 9% compounded annually, what yearly
A family has a $210,000, 20-year mortgage at 6.75% compounded monthly. Find the monthly payment. Also find the unpaid balance after (A) 5 years (B) 10 years (C) 15 years
At the time they retire, a couple has $200,000 in an account that pays 8.4% compounded monthly. (A) If the couple decides to withdraw equal monthly payments for 10 years, at the end of which time the account will have a zero balance, how much should the couple withdraw each month? (B) If the
If the account owner decides to withdraw $3,000 monthly, how much is in the account after 10 years? After 20 years? After 30 years For Information: Refer to Problem 45.
An ordinary annuity pays 6.48% compounded monthly. (A) A person wants to make equal monthly deposits into the account for 15 years in order to then make equal monthly withdrawals of $1,500 for the next 20 years, reducing the balance to zero. How much should be deposited each month for the first 15
A person purchased a house 10 years ago for $160,000. The house was financed by paying 20% down and signing a 30-year mortgage at 7.75% on the unpaid balance. Equal monthly payments were made to amortize the loan over a 30-year period. The owner now (after the 120th payment) wishes to refinance the
A person purchased a $200,000 home 20 years ago by paying 20% down and signing a 30-year mortgage at 13.2% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 10-year mortgage at 8.2% compounded monthly. How much interest will
Discuss the similarities and differences in the graphs of unpaid balance as a function of time for 30-year mortgages of $60,000 at rates of 7%, 10%, and 13%, respectively (see the figure). Include computations of the monthly payment and total interest paid in each case.
A $2,000 computer can be financed by paying $100 per month for 2 years. What is the annual nominal compounding rate for this loan? In Problem, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two
At the time they retire, a couple has $200,000 invested in an annuity. The couple can take the entire amount in a single payment, or receive monthly payments of $2,000 for 15 years. If the couple elects to receive the monthly payments, what annual nominal compounding rate will the couple earn on
Quarterly payments of $610 are made for 6 years to repay loan at 8.24% compounded quarterly. In Problem, find i ( the rate per period) and n ( the number of periods) for each loan at the given annual rate.
Monthly payments of $433 are made for 3 years to repay a loan at 10.8% compounded monthly. In Problem, find i ( the rate per period) and n ( the number of periods) for each loan at the given annual rate.
Solve Problem using substitution y = x - 4 x + 3y = 12
Solve Problem using substitution 3x - y = 7 2x + 3y = 1
Solve Problem using elimination by addition 2x - 3y = -8 5x + 3y = 1
Solve Problem using elimination by addition 2x + 3y = 1 3x - y = 7
Solve problem using substitution or elimination by addition. 4x + 3y = 26 3x - 11y = -7
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