Assume that you plan to retire 40 years from now andthat

For diagrams (a)to(c), compute the unknown valuesB,C,V, using the minimum number of compoundinterest factors

The cash flows have a present value of 0. Computethe value ofJ, assuming a 10% interest rate.

For what value ofn, based on a 31/2% interest rate,do these cash flows have a present value of 0?

The cash flows have a present value of 0. Computethe value ofn, assuming a 10% interest rate.

How much must be deposited now at 51/4% interestto produce$300 at the end of every yearfor 10 years?

A man buys a car for $18,000 with no moneydown. He pays for the car in 30 equal monthly pay-ments with interest at 12% per annum, compoundedmonthly. What is his monthly loan payment?

A car may be purchasedwith a $3000 down paymentnow and 60 monthly paymentsof $480.If the interestrate is 12% compounded monthly, what is the priceof the car?

A company deposits $2000 in a bank at the end ofevery year for 10 years. The company makes nodeposits during the subsequent 5 years. If the bankpays 8% interest, how much would be in the accountat the end of 15 years?

A city engineer knows that she will need $25 millionin 3 years to replace toll booths on a toll road in thecity. Traffic on the road is estimated to be 20 millionvehicles per year. How much per vehicle should thetoll be to cover the cost of the toll booth replacementproject? Interest is 10%. (Simplify your analysis byassuming that the toll receipts are received at the endof each year in a lump sum.

A studentwants to have $30,000atgraduation 4 yearsfrom now to buy a new car. His grandfather gavehim $10,000 as a high school graduation present.How much must the student save each year if hedeposits the $10,000 today and can earn 12% on boththe $10,000 and his earnings in a mutual fund hisgrandfather recommends?

Using linear interpolation, determine the value of(P/A,61/2%,10)from the compoundinterest tables.Compute this same value using the equation or aTVM calculator. Why do the values differ?

How many months will it take to pay off a $525debt, with monthly payments of $15 at the end ofeach month, if the interest rate is 18%, compoundedmonthly?

Tori is planning to buy a car. The maximum paymentshe can make is $3400 per year, and she can get a carloan at her credit union for 7.3% interest. Assume herpayments will be made at the end of each year 14.If Toris old car can be traded in for $3325, whichis her down payment, what is the most expensive carshe can purchase?

A manufacturing firm spends $500,000 annually fora required safety inspection procedure on its pro- duction lines. A new monitoring technology wouldenable the company to eliminate the need for suchinspection. If the interest rate is 10% per year, howmuch can the company afford to spend on this newtechnology?The companywantsto recover its invest-ment in 15 years

A student is buying a new car. The cars price is$16,500,the sales tax is 8%, and thetitle, license, andregistration fee is $450 to be paid in cash. The dealeroffers to finance 90% of the cars price for 48 monthsata nominalinterestrate of 9%peryear,compoundedmonthly.(a)How much cash is paid when the car is pur-chased?(b)How much is the monthly payment?

A student is buying a new car. The cars priceis $19,500, the sales tax is 8%, and thetitle,license, and registration fee is $650 to be paidin cash. Instead of buying the car now, the stu-dent has decided to save money in equal monthlyamounts for 48 months and then pay cash. If thestudent earns 0.75% per month interest on themoney she saves, how much money is the monthlysavings?

Rose recently graduated in engineering. Her employ-er will give her a raise of $3500 per year if she passesthe FE exam (Fundamentals of Engineering). Over acareer of 40 years, what is the present worth of theraise if the interest rate is 7%?

Jose graduated in engineering 5 years ago. Hisemployer will give him a raise of $10,000 per year ifhe passes the PE exam (Professional Engineer). Overa career of 35 years, what is the present worth of theraise if the interest rate is 8%?

Brad will graduate next year. When he begins work-ing, he plans to deposit $3000 at the end of each yearinto an IRA account. If the retirement account pays4% interest, how much will be in his accountafter 40deposits?

If the universitys College of Engineering can earn4% on its investments,how much should be in its sav-ings accountto fund one $5000scholarship each yearfor 10 years?

Elias makes 7 annual end-of-year deposits of $350into an account earning 2.5% interest. How much isin the account at the end of Year 11, if he makes noadditional deposits and makes no withdrawals?

Liam dreams of starting his own business to importconsumer electronic products to his home country.He estimates he can earn 5% on his investments andthat he will need to have $300,000 at the end ofyear 10 if he wants to give his business a good solidfoundation. He now has $28,850 in his account, andhe believes he can save $12,000 each year from hisincome, beginning now. He plans to marry at aboutthe end of year 6 and will skip the investment contri-bution thatyear.How far belowor abovehis $300,000goal will he be?

Martin pays rent of $500 per month for the 9-monthacademic year. He is going to travel the world thissummer and wont be working. How much must heset aside in his savings accountfor the 3-month sum-mer to cover his rent for next year? The savingsaccount earns 3% with monthly compounding.

How much money should Timothy and Tiffanydeposit annually for 20 years in order to provide anincome of $30,000 per year for the next 10 years?Assume the interest rate is a constant 4%.

LaQuita deposits $3500 in her retirement accountevery year.If heraccountpaysan averageof6%inter- est and she makes 38 deposits before she retires, howmuch money can she withdraw in 20 equal paymentsbeginning one year after her last deposit?

Determine the breakeven resale price 10 years fromnow of an apartment house that can be bought todayfor $449,000. Its annual net income is $54,000. Theowner wants a 10% annual return on her investment.

Kelsey Construction has purchased a crane thatcomes with a 3-year warranty. Repair costs areexpectedto average $3500per yearbeginning in Year4 when the warranty expires. Determine the presentworth of the cranes repair costs over its 15-year life.The interest rate is 10%

A young engineer wishes to become a millionaire bythe time he is 60 years old. He believes that by careful investmenthe can obtain a 15% rate of return.He plans to add a uniform sum of money to hisinvestment program each year, beginning on his 20thbirthday and continuing through his 59thbirthday.How much money must the engineer set aside in thisproject each year?

What amount will be required to purchase, on anengineerss 40thbirthday, an annuity to provide himwith 30 equal semiannual payments of $1000 each,the first to be received on his 50thbirthday,if nominalinterest is 4% compounded semiannually?

The first of a series of equal semiannual cash flowsoccurs on July 1, 2011, and the last occurs on Jan-uary 1, 2024. Each cash flow is equal to $128,000.The nominal interest rate is 12% compounded semi-annually. What single amount on July 1, 2015 isequivalent to this cash flow system?

On January 1, Frank Jenson bought a used carfor $7200 and agreed to pay for it as follows:1/3down payment; the balance to be paid in 36 equalmonthly payments; the first payment due Febru-ary 1; an annual interest rate of 9%, compoundedmonthly.(a)What is the amountof Franks monthly payment?(b)During the summer, Frank made enough moneyto pay off the entire balance due on the caras of October 1. How much did Frank owe onOctober 1?

Ifi=12%, for what value ofBis the presentvalue=0

ComputeEso that the cash flows have a presentvalue of 0

A man borrowed $500 from a bank on October15th. He must repay the loan in 16 equal monthlypayments, due on the 15thof each month, begin-ning November 15th. If interest is computed at 1%per month, how much must he pay each month?

Jerry bought a house for $500,000 and made a$100,000 down payment. He obtained a 30-yearloan for the remaining amount. Payments were mademonthly. The nominal annual interest rate was 9%.After 10 years (120 payments) he decided to pay theremaining balance on the loan.(a)What was his monthly loan payment?(b)What must he have paid (in addition to his regu-lar 120thmonthly payment) to pay the remainingbalance of his loan?

A man wants to help provide a college education forhis young daughter. He can afford to invest $600/yrfor the next 4 years, beginning on the girls 4thbirthday. He wishes to give his daughter $4000 onher 18th,19th,20th, and 21stbirthdays, for a totalof $16,000. Assuming 5% interest, what uniformannual investment will he have to make on the girls8ththrough 17thbirthdays?

Table 3-1 presented four plans for the repayment of$5000 in 5 yearswith interest at8%. Still another wayto repay the $5000would be to makefour annualend-of-year payments of $1000 each, followed by a finalpaymentat the end of the fifth year. How much wouldthe final payment be

A $150 bicycle was purchased on December 1 witha $15 down payment. The balance is to be paid atthe rate of $10 at the end of each month, with thefirst payment due on December 31. The last paymentmay be some amount less than $10. If interest on theunpaid balance is computed at 11/2% per month, howmany payments will there be, and what is the amountof the final payment?

A company buys a machine for $12,000, which itagrees to pay for in five equal annual payments,beginning one year after the date of purchase, at anannual interest rate of 4%. Immediately after the sec-ond payment, the terms of the agreementare changedto allow the balancedue to be paid off in a single pay-ment the next year. What is the final single payment?

An engineering student bought a car at a local usedcar lot. Including tax and insurance, the total pricewas $6000. He is to pay for the car in 12 equalmonthly payments, beginning with the first payment immediately (in other words, the first payment wasthe down payment). Nominal interest on the loanis 12%, compounded monthly. After six payments(the down payment plus five additional payments),he decides to sell the car. A buyer agrees to pay acash amount to pay off the loan in full at the time thenext payment is due and also to pay the engineeringstudent $2000.If there are no penalty charges for thisearly paymentof the loan, how much will the car costthe new buyer?

A realtor sold a house on August 31, 2011, for$150,000 to a buyer in which a 20% down paymentwas made. The buyer took a 15-year mortgage onthe property with an effective interest rate of 8% perannum. The buyer intends to pay off the mortgageowedin yearly paymentsstarting on August31,2012.(a)How much of the mortgage will still be owedafter the payment due on August 31, 2018, hasbeen made?(b)Solve the sameproblemby separating the interestand the principal amounts.

To provide for a college education for her son, awoman opened an escrow account in which equaldeposits were made. The first deposit was made onJanuary 1, 1995, and the last deposit was made onJanuary 1, 2012. The yearly college expensesinclud-ing tuition were estimated to be$8000, for each ofthe 4 years. Assuming the interest rate to be 5.75%,how much did the mother have to deposit each yearin the escrow account for the son to draw $8000 peryear for 4 years beginning January 1, 2012?

A bank recently announcedan instant cash plan forholders of its bank credit cards. A cardholder mayreceive cash from the bank up to a preset limit (about$500). There is a special charge of 4% made at thetime the instant cash is sent to the cardholders. Thedebt may be repaid in monthly installments. Eachmonth the bank charges 11/2% on the unpaid balance.The monthly payment, including interest, may be aslittle as$10. Thus, for $150 of instant cash, an ini-tial chargeof$6 is madeand addedto thebalancedue.Assume the cardholder makes a monthly payment of$10 (this includes both principal and interest). Howmany months are required to repay the debt? If youranswerincludesa fraction of a month, round up to thenext month.

An engineer borrowed $3000 from the bank, payablein six equal end-of-year payments at 8%. The bankagreed to reduce the interest on the loan if interestrates declined in the U.S. before the loan was fullyrepaid. At the end of 3 years, at the time of the third payment, the bank agreed to reduce the interest rateon the remaining debt from 8% to 7%. What was theamount of the equal annualend-of- year payments foreach of the first 3 years? What was the amount ofthe equalannualend-of- yearpaymentsfor eachof thelast 3 years?

A local finance company will loan $10,000 to ahomeowner.It is to be repaid in 24 monthly paymentsof $499 each. The first payment is due 30 days afterthe $10,000 is received. What interest rate per monthare they charging

A woman made 10 annual end-of-year purchases of$1000 worth of common stock. The stock paid nodividends. Then for 4 years she held the stock. Atthe end of the 4 years she sold all the stock for$28,000. What interest rate did she obtain on herinvestment?

For some interest rateiand some number of interestperiodsn, the uniform series capital recovery factoris 0.1408 and the sinking fund factor is 0.0408. Whatis the interest rate? What isn?

For some interest rateiand some number of interestperiodsn, the uniform series capital recovery factoris 0.1728 and the sinking fund factor is 0.0378. Whatis the interest rate?

Derive an equation to find the end-of-year futuresumFthat is equivalent to a series ofnbeginning-of- year paymentsBat interest ratei.Thenusetheequation to determine the future sumFequivalentto sixBpayments of $100 at 8% interest. (Answer:F=$792.28

If $200 is deposited in a savings accountat the begin-ning of each of 15 years, and the account drawsinterest at 7% per year, how much will be in theaccount at the end of 15 years?

How can the tables be used to compute (P/A,5%,150)? (P/A, 7%, 200)?

Prove the following relationships algebraically(a)(A/F,i,n)=(A/P,i,n)i(b)(P/F,i,n)=(P/A,i,n)(P/A,i,n1)(c)(P/A,i,n)=(P/F,i,1)+(P/F,i,2)++(P/F,i, n)(d)(F/A,i,n)=[(F/P,i,n)1]/i

Assume a 10% interest rate and findS,T,andx.

Compute the unknown values

For diagrams (a)to(d), compute the present valuesof the cash flows.

Compute the present value of the cash flows.

Use a 15% interest rate to compute the present valueof the cash flows

The cash flows have a present value of 0. Computethe value ofC, assuming a 10% interest rate.

If i=12%, for what value ofGdoes the presentvalue equal 0?

The cashflowshave a presentvalue equal0. Computethe value ofDin the diagram

Using a 10% interest rate, for what value ofBdoesthe present value equal 0?

These cash flow transactions are said to be equivalentin terms of economic desirability at an interest rate of12% compounded annually. Determine the unknownvalueA

For what value ofPin the cash flow diagram doesthe present value equal 0?

Use a 10% interest rate to compute the present valueof the cash flows

Consider the following cash flow:Year Cash Flow0$1001502603704805 140Which one of the following is correct for this cashflow?A.100=50+10(A/G,i,5)+50(P/F,i,5)B.1=50(P/A,i,5)+10(P/G,i,5)+50(P/F,i,5)100C.100(A/P,i,5) =50+10(A/G,i,5)D.None of the equations are correct

Consider the following cash flow:Year Cash Flow0$P1 10002 8503 7004 5505 4006 4007 4008 400Alice was asked to compute the value ofPfor thecashflow at8% interest. She wrote three equations:A.P=1000(P/A,8%,8)150(P/G,8%,8)+150(P/G,8%,4)(P/F,8%,4)B.P=400(P/A,8%,8)+600(P/ A,8%,5)150(P/G,8%,4)C.P=150(P/G,8%,4)+850(P/A,8%,4)+400(P/A,8%,4)(P/F,8%,4)Which of the equations is correct?

It is estimated that the maintenance cost on a newcar will be $400 the first year. Each subsequentyear,this cost is expected to increase by $100. How muchwould you need to set aside when you bought a newcar to pay all future maintenance costs if you plannedto keep the vehicle for 7 years? Assume interest is 5%per annum

The council members of a small town have decidedthat the earth levee that protects the town floodingshould be rebuilt and strengthened. The town engi-neer estimates that the cost of the work at the end ofthe first year will be $85,000. He estimates that insubsequent years the annual repair costs will declineby $10,000, making the second-year cost $75,000;the third-year $65,000, and so forth. The councilmembers want to know what the equivalent presentcost is for the first 5 years of repair work if interest is4%

A firm expects to install smog control equipment onthe exhaustof a gasoline engine.The local smog con-trol district has agreed to pay to the firm a lump sumof money to provide for the first costof the equipmentand maintenance during its 10-year useful life. At theend of 10 years the equipment, which initially cost$10,000, is valueless. The firm and the smog controldistrict have agreed that the following are reasonableestimates of the end-of-year maintenance costs Year$500 Year 6 $2002 100 7 2253 125 8 2504 150 9 2755 175 10 300Assuming interest at 6% per year, how much shouldthe smog control district pay to the firm now toprovide for the first cost of the equipment and itsmaintenance for 10 years

A debt of $5000 can be repaid, with interest at 8%,by the following paymenPayment1 $ 5002 10003 15004 20005XThe payment at the end of the fifth year is shown asX.HowmuchisX?

A man is buying a small garden tractor. There will beno maintenance cost during the first 2 years becausethe tractor is sold with 2 years free maintenance. Forthe third year, the maintenance is estimated at $80. Insubsequent years the maintenance cost will increaseby $40 peryear.How much would needto be setasidenow at 8% interest to pay the maintenance costs onthe tractor for the first 6 years of ownership?

A woman makes an investment every 3 months ata nominal annual interest rate of 28%, compoundedquarterly. Her first investment was $100, followedby investmentsincreasing$20 each 3 months. Thus,the second investment was $120, the third invest-ment $140, and so on. If she continues to make thisseries of investments for a total of 20 years, whatwill be the value of the investments at the end of thattime?

A sports star can sign a 6-year contract that startsat $1.2M with increases of $0.3M each year for hisexpected playing career of 6 years. It is also possibleto sign a contract that starts at $0.8M for the first yearand then increases at $0.2M each year for 10 years(note some income is deferred until after he retires).If his interest rate for the time value of money is 8%,what is the value of each choice?

A college student is buying a new car, which costs$16,500 plus 8% sales tax. Thetitle, license, andregistration fees are $650. The dealer offers her afinancing program that starts with a small monthlypayment, and the payments will gradually increase.The dealer offers to finance80% of the cars price for48 months at a nominal interest rate of 9% per year,compounded monthly. The first payment is $300 andeach successive payment will increase by a constantdollaramountx.(a)How much is the constant amountx?(b)How much is the 48thpayment?

A firm has $500,000 per year to pay for replac-ing machinery over the next 5 years. What is theexpected cost in Year 1 if the firm has projected thatthe machinery costwill increase by $15,000peryear?The interest rate is 10% per year.

A construction firm can achieve a $15,000 cost sav-ings in Year 1 and increasing by $2000 each year forthe next 5 years by upgrading some equipment. Atan interest rate of 15%, what is the equivalent annualworth of the savings?

Helen can earn 3% interest in her savings account.Her daughter Roberta is 11 years old today. SupposeHelen deposits $4000 today, and one year from todayshe deposits another $500. Each year she increasesher deposit by $500 until she makes her last depositon Robertas 18thbirthday. What is the annual equiv-alent of her deposits, and how much is on depositafter the 18thbirthday?

Francisco believes in planning ahead. So he decidesto find out how much he can draw from a retirementaccount each year for 30 years if he invests exactly$1000 each year in the account. Suppose that he canearn 5% on this long-term account, that he will make40 deposits,andthat he will makethe firstwithdrawalone year after the last deposit. How big can Fran-ciscos withdrawals be?

Perry is a freshman. He estimates that the cost oftuition, books, room and board, transportation, andotherincidentalswill be $13,000this year.He expectsthesecoststo rise about$1500eachyearwhile he is incollege.Ifitwilltakehim5yearstoearnhisBS,whatisthe presentcostof his degree atan interest rate of 6%?Ifheearnsanextra$10,000annuallyfor40years,whatis the presentworth ofhis degree?

The following cash flows are equivalent in value ifthe interest rate isi. Which one is more valuable ifthe interest rate is 2i?

The following cash flows are equivalent in value ifthe interest rate isi. Which one is more valuable ifthe interest rate is 2i?

A set of cash flows begins at $20,000 the first year,with an increase each year untiln=10 years. If theinterest rate is 8%, what is the present value when(a)the annual increase is $2000?(b)the annual increase is 10%?

A set of cash flows begins at $50,000 the first year,with an increase each year untiln=15 years. If theinterest rate is 7%, what is the present value when(a)the annual increase is $5000?(b)the annual increase is 10%?

A set of cash flows begins at $20,000 the first year,with an increase each year untiln=10 years. If theinterest rate is 10%, what is the present value when(a)the annual increase is $2000?(b)the annual increase is 10%?

A set of cash flows begins at $20,000 the first year,with a decrease each year untiln=10 years. If theinterest rate is 8%, what is the present value when(a)the annual decrease is $2000?(b)the annual decrease is 10%?'

The market for a product is expected to increase atan annualrate of 8%. First-year sales are estimated at$60,000, the horizon is 15 years, and the interest rateis 10%. What is the present value?

Fred is evaluating whether a more efficient motorwith a life of 5 years should be installed on an assem-bly line. Energy savings are estimated at $400 for thefirst year, then increasing by 6% annually.If the inter-est rate is 10%, what is the presentvalue of the energysavings?

In Problem 4-87, what if the energy savings areincreasing by 15% annually?

Suzanne is a recent chemical engineering graduatewho has been offered a 5-year contract at a remotelocation. She has been offered two choices. The firstis a fixed salary of $75,000 per year. The second hasa starting salary of $65,000 with annual raises of 5%starting in Year 2. (For simplicity, assume that hersalary is paid at the end of the year, just before herannual vacation.) If her interest rate is 9%, whichshould she take?

Mark Johnson saves a fixed percentage of his salaryat the end of each year. This year he saved $1500.Forthe next 5 years, he expects his salary to increase atan 8% annual rate, and he plans to increase his sav-ings at the same8% annualrate. He invests his moneyin the stock market. Thus there will be six end-of-year investments (the initial$1500 plus five more).Solve the problem using the geometric gradientfactor.(a)How much will the investments be worth at theend of 6 years if they increase in the stock marketat a 10% annual rate?(b)How much will Mark have at the end of 6 yearsif his stock market investments increase only at8% annually?

The Macintosh Company has an employee savingsplan that allows every employee to invest up to 5%of his or her annual salary. The money is invested incompany common stock with the company guaran-teeing that the annual return will never be less than8%. Jill was hired at an annualsalary of $52,000. Sheimmediately joined the savingsplan investing the full5% of her salary each year. If Jills salary increases atan 8%uniform rate, and she continuesto invest 5% ofit each year,what amountof money is she guaranteedto have at the end of 20 years?

The football coach at a midwestern universitywas given a 5-year employment contract that paid$225,000 the first year, and increased at an 8%uniform rate in each subsequent year. At the end ofthe first years football season, the alumni demandedthat the coach be fired. The alumni agreed to buyhis remaining years on the contract by paying himthe equivalent present sum, computed using a 12%interest rate. How much will the coach receive?

A25-year-oldengineerisopeninganindividualretire-ment account(IRA) at a bank.Her goal is to accumu- late $1 million in theaccount by the time she retiresfrom work in 40 years. The bank manager estimatesshe may expect to receive 8% nominal annual inter-est, compounded quarterly, throughout the 40 years.Theengineerbelievesherincomewillincreaseata7%annual rate during her career. She wishes to start herIRA with as low a deposit as possible and increase itata7%rateeachyear.Assumingend-of-yeardeposits,howmuchshouldshedepositthefirstyear?

A contractor estimates maintenance costs for a newbackhoeto be $275 for the first month with a monthlyincrease of 0.5%. The contractor can buy a 4-yearmaintenance contract for $18,500 at any point. If thecontractispurchasedatthesametimeasthebackhoeispurchased,the dealerhasoffered a 10%discount.Usei=0.75%permonth.Whatshouldthecontractordo?

An engineer will deposit 15% of her salary each yearinto a retirement fund. If her current annual salary is$80,000 and she expects that it will increase by 5%each year, what will be the present worth of the fundafter 35 years if it earns 5% per year?

Zachary has opened a retirement account that willpay 5% interest each year. He plans to deposit 10%of his annual salary into the account for 39 yearsbefore he retires. His first years salary is $52,000,and he expects the salary to grow 4% each year. Howmuch will be in his account after he makes the lastdeposit? Whatuniform amountcanhe withdraw fromthe account for 25 years beginning one year after hislast deposit?

Eddie is a production engineer for a major sup-plier of component parts for cars. He has determinedthat a robot can be installed on the production lineto replace one employee. The employee earns $20per hour and benefits worth $8 per hour for a totalannual cost of $58,240 this year. Eddie estimatesthis cost will increase 6% each year. The robot willcost $16,500 to operate for the first year with costsincreasing by $1500eachyear. Thefirm usesan inter-est rate of 15% and a 10-year planning horizon. Therobot costs $75,000 installed and will have a sal-vage value of $5000 after 10 years. Should Eddierecommend that purchase of the robot?

Quentin has been using his credit card too much. Hisplan is to use only cash until the balance of $8574is paid off. The credit card company charges 18%interest, compounded monthly. What is the effec-tive interest rate? How much interest will he owein the first months payment? If he makes monthlypayments of $225, how long until it is paid off?

A bank is offering a loan of $25,000 with a nominalinterest rate of 18% compoundedmonthly, payablein60 months.(Hint:The loan origination fee of 2% willbe taken out from the loan amount.)(a)What is the monthly payment?(b)If a loan origination fee of 2% is charged at thetime of the loan, what is the effective interestrate?

One of the largest car dealers in the city advertises a3-year-old car for sale as follows:Cash price $13,750, or a down paymentof $1375 with 45 monthly payments of$361.23.Susan DeVaux bought the car and made a downpayment of $2000. The dealer charged her the sameinterest rate used in his advertised offer. What is themonthly interest rate? How muchwill Susanpay eachmonth for 45 months? What effective interest rate isbeing charged?

Pete borrows $10,000 to purchase a used car. Hemust repay the loan in 48 equal end-of- periodmonthly payments. Interest is calculated at 11/4%per month. Determine the following:(a)The nominal annual interest rate(b)The effective annual interest rate(c)The amount of the monthly payment

Picabo borrows $1000. To repay the amount, shemakes 12 equal monthly payments of $90.30. Deter- mine the following:(a)The effective monthly interest rate(b)The nominal annual interest rate(c)The effective annual interest rate

TheBawl Street Journalcosts $580, payable now,for a 2-year subscription.The newspaperis published252 days per year (5 days per week, except holidays).If a 10% nominal annual interest rate, compoundedquarterly, is used:(a)What is the effective annual interest rate in thisproblem?

You are taking a $2000 loan. You will pay it backin four equal amounts, paid every 6 months starting3 years from now. The interest rate is 6% com-pounded semiannually. Calculate:(a)The effective interest rate, based on both semi-annual and continuous compounding(b)The amount of each semiannual payment(c)The total interest paid

In 1555 King Henry borrowed money from hisbankers on the condition that he pay 5% of the loanat each fair (there were four fairs per year) until hehad made 40 payments. At that time the loan wouldbe considered repaid. What effective annual interestdid King Henry pay

A local bank offers a customer a 2-year car loan of$10,000 as follows:Money to pay for car$10,000Two years interest at 7%: 20.0710,000 1400$11,40024 monthly payments=11,40024=$475.00The first payment must be made in 30 days. What isthe nominalannualinterestrate the bankis receiving?

A local lending institution advertises the 5150Club. A person may borrow $2000 and repay $51 forthe next 50 months, beginning 30 daysafter receivingthe money. Compute the nominal annual interest ratefor this loan. What is the effective interest rate?

TheRule of 78sis a commonly used method of com-puting the amount of interest when the balance of aloan is repaid in advance.Adding the numbers representing12 months gives1+2+3+4+5++11+12=78If a 12-month loan is repaid at the endof one month, for example, the interestthe borrower would be charged is 12/78of the years interest. If the loan is repaidat the end of 2 months, the total interestcharged would be(12+11)/78, or 23/78of the years interest. After 11 months theinterestcharge would therefore be 77/78ofthe total years interest.Helen borrowed $10,000 on January 1 at 9% annualinterest, compounded monthly. The loan was to berepaid in 12 equal end-of- period payments. Helen made the firsttwo payments and then decidedto repaythe balance of the loan with the third payment. Thusshewillpaythethirdpaymentplusanadditionalsum.You are to calculate the amount of this addit-ional sum(a)based on the rule of 78s.(b)based on exact economic analysis methods.

Upon the birth of his first child, Dick Jonesdecidedtoestablish a savings account to partly pay for his sonseducation. He plans to deposit $20 per month in theaccount, beginning when the boy is 13 months old.The savings and loan association has a current inter-est policy of 6% per annum, compounded monthly,paid quarterly. Assuming no change in the interestrate, how much will be in the savings account whenDicks son becomes 16 years old?

Ann deposits $100 at the end of each month into herbank savings account. The bank paid 6% nominalinterest, compounded and paid quarterly. No interestwas paid on money not in the account for the full 3-month period. How much was in Anns accountat theend of 3 years

What is the present worth of a series of equal quar-terly payments of $3000 that extends over a periodof 8 years if the interest rate is 10% compoundedmonthly?

What single amount on April 1, 2012, is equivalent toa series of equal,semiannualcashflows of $1000 thatstarts with a cash flow on January 1, 2010, and endswith a cash flow on January 1, 2019? The interest rateis 14% and compounding is quarterly

A contractor wishes to set up a special fund bymaking uniform semiannual end-of-period depositsfor 20 years. The fund is to provide $10,000 at theend of each of the last 5 years of the 20-year period.If interest is 8%, compounded semiannually, what isthe required semiannual deposit?

Pacos saving account earns 13% compoundedweekly and receives quarterly deposits of $38,000.His first deposit occurred on October 1, 2006, and thelast deposit is scheduled for April 1, 2022. Tishasaccount earns 13% compounded weekly. Semian-nual deposits of $18,000 are made into her account,with the first one occurring on July 1, 2016, and thelast one occurring on January 1, 2025. What singleamount on January 1, 2017, is equivalent to the sumof both cash flow series?

The first of a series of equal monthly cash flows of$2000 occurred on April 1, 2008, and the last of themonthly cash flows occurred on February 1, 2010. This series of monthly cash flows is equivalent to aseries of semiannualcash flows. The first semiannualcash flow occurred on July 1, 2011, and the lastsemiannual cash flow will occur on January 1, 2020.What is the amount of each semiannual cash flow?Use a nominal interest rate of 12% with monthlycompounding on all accounts.

A series of monthly cash flows is deposited into anaccountthat earns 12%nominalinterest compoundedmonthly.Eachmonthly depositis equalto $2100.Thefirst monthly deposit occurred on June 1, 2008 andthe last monthly deposit will be on January 1, 2015.The account (the series of monthly deposits, 12%nominal interest, and monthly compounding) alsohas equivalentquarterly withdrawals from it. The firstquarterly withdrawal is equal to $5000 and occurredon October 1, 2008. The last $5000 withdrawal willoccur on January 1, 2015. How much remains in theaccount after the last withdrawal?

PARC Company has money to invest in an employeebenefit plan, and you have been chosen as the planstrustee. As an employee yourself, you want to maxi-mize the interest earned on this investment and havefound an accountthat pays 14% compoundedcontin- uously.PARCisprovidingyou$1200permonthtoputinto youraccountfor7 years.Whatwillbe the balanceinthisaccountattheendofthe7-yearperiod?

Barry, a recentengineeringgraduate,nevertook engi-neering economics.When he graduated,he was hiredby a prominent architectural firm. The earnings fromthis job allowed him to deposit $750 each quar-ter into a savings account. There were two banks thatoffered savings accounts in his town (a small town!).The first bank was offering 4.5% interest com-pounded continuously. The second bank offered4.6% compoundedmonthly. Barry decidedto depositin the first bank because it offered continuous com-pounding. Did he make the right decision?

What single amount on October 1, 2012, is equalto a series of $1000 quarterly deposits made into anaccount? The first deposit occurs on October 1, 2012,and the last deposit occurs on January 1, 2026. Theaccount earns 13% compounded continuously

Develop a complete amortization table for a loanof $4500, to be paid back in 24 uniform monthlyinstallments, based on an interest rate of 6%.The amortization table must include the followingcolumn headings: made the firsttwo payments and then decidedto repaythe balance of the loan with the third payment. Thusshewillpaythethirdpaymentplusanadditionalsum.You are to calculate the amount of this addit-ional sum(a)based on the rule of 78s.(b)based on exact economic analysis methods.

Upon the birth of his first child, Dick Jonesdecidedtoestablish a savings account to partly pay for his sonseducation. He plans to deposit $20 per month in theaccount, beginning when the boy is 13 months old.The savings and loan association has a current inter-est policy of 6% per annum, compounded monthly,paid quarterly. Assuming no change in the interestrate, how much will be in the savings account whenDicks son becomes 16 years old?

Ann deposits $100 at the end of each month into herbank savings account. The bank paid 6% nominalinterest, compounded and paid quarterly. No interestwas paid on money not in the account for the full 3-month period. How much was in Anns accountat theend of 3 years?

What is the present worth of a series of equal quar-terly payments of $3000 that extends over a periodof 8 years if the interest rate is 10% compoundedmonthly?

What single amount on April 1, 2012, is equivalent toa series of equal,semiannualcashflows of $1000 thatstarts with a cash flow on January 1, 2010, and endswith a cash flow on January 1, 2019? The interest rateis 14% and compounding is quarterly

A contractor wishes to set up a special fund bymaking uniform semiannual end-of-period depositsfor 20 years. The fund is to provide $10,000 at theend of each of the last 5 years of the 20-year period.If interest is 8%, compounded semiannually, what isthe required semiannual deposit?

Pacos saving account earns 13% compoundedweekly and receives quarterly deposits of $38,000.His first deposit occurred on October 1, 2006, and thelast deposit is scheduled for April 1, 2022. Tishasaccount earns 13% compounded weekly. Semian-nual deposits of $18,000 are made into her account,with the first one occurring on July 1, 2016, and thelast one occurring on January 1, 2025. What singleamount on January 1, 2017, is equivalent to the sumof both cash flow series?

The first of a series of equal monthly cash flows of$2000 occurred on April 1, 2008, and the last of themonthly cash flows occurred on February 1, 2010. This series of monthly cash flows is equivalent to aseries of semiannualcash flows. The first semiannualcash flow occurred on July 1, 2011, and the lastsemiannual cash flow will occur on January 1, 2020.What is the amount of each semiannual cash flow?Use a nominal interest rate of 12% with monthlycompounding on all accounts.

PARC Company has money to invest in an employeebenefit plan, and you have been chosen as the planstrustee. As an employee yourself, you want to maxi-mize the interest earned on this investment and havefound an accountthat pays 14% compoundedcontin- uously.PARCisprovidingyou$1200permonthtoputinto youraccountfor7 years.Whatwillbe the balanceinthisaccountattheendofthe7-yearperiod?

Barry, a recentengineeringgraduate,nevertook engi-neering economics.When he graduated,he was hiredby a prominent architectural firm. The earnings fromthis job allowed him to deposit $750 each quar-ter into a savings account. There were two banks thatoffered savings accounts in his town (a small town!).The first bank was offering 4.5% interest com-pounded continuously. The second bank offered4.6% compoundedmonthly. Barry decidedto depositin the first bank because it offered continuous com-pounding. Did he make the right decision?

What single amount on October 1, 2012, is equalto a series of $1000 quarterly deposits made into anaccount? The first deposit occurs on October 1, 2012,and the last deposit occurs on January 1, 2026. Theaccount earns 13% compounded continuously.

Develop a complete amortization table for a loanof $4500, to be paid back in 24 uniform monthlyinstallments, based on an interest rate of 6%.The amortization table must include the followingcolumn headings: made the firsttwo payments and then decidedto repaythe balance of the loan with the third payment. Thusshewillpaythethirdpaymentplusanadditionalsum.You are to calculate the amount of this addit-ional sum(a)based on the rule of 78s.(b)based on exact economic analysis methods.

Using the loan and payment plan developed inProblem 4-120, determine the month that the finalpayment is due, and the amount of the final payment,if $500 is paid for Payment 8 and $280 is paid forPayment10. This problemrequires a separateamorti- zationtablegivingthebalancedue,principalpayment,andinterestpaymentforeachperiodoftheloan

The following beginning-of-month (BOM) and end-of-month (EOM) amounts are to be deposited ina savings account that pays interest at 9%, com-pounded monthly:Today (BOM 1) $400EOM 2270EOM 6100EOM 7180BOM 10 200Set up a spreadsheet to calculate the account balanceat the end of the first year (EOM12). The spread-sheet must include the following column headings:Month Number, Deposit BOM, Account Balance atBOM, Interest Earned in Each Month, Deposit EOM,Account Balance at EOM. Also, use the compoundinteresttablestodrawacashflowdiagramofthisprob- lemandsolvefortheaccountbalanceattheEOM12.

What is the present worth of cash flows that begin at$20,000 and increase at 7% per year for 10 years?The interest rate is 9%.

What is the present worth of cash flows that begin at$50,000 and decrease at 12% per year for 10 years?The interest rate is 8%

Net revenues at an older manufacturing plant will be$2 million for this year. The net revenue will decrease15%peryearfor5 years,whentheassembly plantwillbeclosed(attheendofYear6).Ifthefirmsinterestrateis10%,calculatethePWoftherevenuestream

What is the present worth of cash flows that begin at$10,000 and increase at 8% per year for 4 years? Theinterest rate is 6%

What is the present worth of cash flows that begin at$30,000 and decrease at 15% per year for 6 years?The interest rate is 10%.

Five annual payments at an interest rate of 9% aremade to repay a loan of $6000. Build the tablethat shows the balance due, principal payment, andinterest payment for each payment. What is theannual payment? (Use a spreadsheet function, notthe tables.) What interest is paid in the last year?

A newly graduated engineer bought furniture for$900 from a local store. Monthly payments for 1year will be made. Interest is computed at a nomi-nal rate of 6%. Build the table that shows the bal- ancedue,principalpayment,and interestpaymentforeach payment. What is the monthly payment? (Use aspreadsheetfunction, not the tables.) What interest ispaid in the last month?

Calculate and print out the balance due, principalpayment, and interest payment for each period of aused-car loan. The nominal interest is 12% per year,compounded monthly. Payments are made monthlyfor 3 years. The original loan is for $11,000.

Calculate and print out the balance due, principalpayment, and interest payment for each period of anew car loan. The nominal interest is 9% per year,compounded monthly. Payments are made monthlyfor 5 years. The original loan is for $17,000

For the used car loan of Problem 4-130, graph themonthly payment.(a)As a function of the interest rate (515%).(b)Asafunctionofthenumberofpayments(2448)

For the new car loan of Problem 4-131, graph themonthly payment.(a)As a function of the interest rate (414%).(b)Asafunctionofthenumberofpayments(3684)

Your beginning salary is $50,000. You deposit 10%at the end of each year in a savings account thatearns 6% interest. Your salary increases by 5% peryear. What value does your savings book show after40 years?

The market volume for widgets is increasing by 15%per year from current profits of $200,000. Investingin a design change will allow the profit per widget tostay steady; otherwise profits will drop 3% per year.What is the present worth of the savingsover the next5 years? Ten years? The interest rate is 10%

A 30-year mortgage for $120,000 has been issued.The interest rate is 10% and payments are mademonthly. Print out the balance due, principal pay-ment, and interest payment for each period

A homeowner may upgrade a furnace that runs onfuel oil to a natural gas unit. The investment will be $2500 installed. The cost of the natural gas willaverage $60 per month over the year, instead of the$145 per month that the fuel oil costs. If the interestrate is 9% per year, how long will it take to recoverthe initial investment?

Develop a general-purpose spreadsheet to calculatethe balance due, principal payment, and interest pay-ment for each period of a loan. The user inputs to thespreadsheet will be the loan amount, the number ofpayments per year, the number of years payments aremade, and the nominal interest rate. Submit printoutsof your analysis of a loan in the amount of $15,000 at8.9%nominalrate for36 months and for60 months ofpayments

Use the spreadsheet developed for Problem 4-138 toanalyze 180-month and 360-month house loan pay-ments. Analyze a $100,000 mortgage loan at a nom-inal interest rate of 7.5% and submit a graph of theinterest and principal paid over time. You need notsubmit the printout of the 360 payments because itwill not fit on one page

Assume that you plan to retire 40 years from now andthat you expect to need $2M to support the lifestylethat you want.(a)If the interest rate is 10%, is the following state-mentapproximately true? Waiting 5 years to startsavingdoubleswhatyoumustdepositeachyear.(b)Ifthe interestrate is 12%,is the required multiplierhigherorlowerthanforthe5%ratein(a)?(c)At what interest rate is the following statementexactly true? Waiting 5 years to start savingdoubles what you must deposit each year.

For winners of the California SuperLotto Plus, thechoice is between a lump sum and annual paymentsthat increase from 2.5% for the first year to 2.7% forthe second year and then increase by 0.1% per yearto 5.1% for the 26thpayment. The lump sum is equalto the net proceeds of bonds purchased to fund the26 payments. This is estimated at 45% to 55% of thelump sum amount. At what interest rate is the presentworth ofthe two paymentplans equivalentif the lumpsum is 45%? If it is 55%?