Assume that you save 1 penny a day for 50 years,that you

Explain the difference between simple and com-pound interest. Which is more common?

A woman borrowed $2000 and agreed to repay it atthe end of 3 years, together with 10% simple interestper year. How much will she pay 3 years hence?

A $5000loan was to be repaid with 8% simple annualinterest. A total of $5350 was paid. How long had theloan been outstanding?

At an interest rate of 10% per year, $100,000 today isequivalent to how much a year from now?

A company invested $450,000 ten years ago in a newtechnology that is now worth $1,000,000. What rateof interest did the company earn on a simple interestbasis?

How long will it take for an investment to double ata 4% per year simple interest rate?

In your own words explain thetime value of money.From your own life (either now or in a situationthat might occur in your future), provide an exam-ple in which the time value of money would beimportant

Which is more valuable, $20,000 received now or$5000 per year for 4 years? Why?

Magdalen, Miriam, and Mary June were asked toconsider two different cash flows: $500 that theycould receive today and $1000 that would be received 3 years from today. Magdalen wanted the $500 dol-lars today, Miriam chose to collect $1000 in 3 years,and Mary June was indifferent between these twooptions. Can you offer an explanation of the choicemade by each woman?

How long will it take for an investment to double at4% per year compounding annually?

A firm has borrowed $5,000,000 for 5 years at 10%per year compound interest. The firm will make nopayments until the loan is due, when it will pay offthe interest and principal in one lump sum. What isthe total payment?

Assume that you save 1 penny a day for 50 years,that you deposit it in the bank at the end of eachmonth, and that there are 30.5 days per month (yousave 30.5 cents each month). How much do you haveafter 50 years, if:(a)The bank does not pay any interest.(b)The bank pays 2% per month interest.

A manufacturing company made an investment 10years ago that is now worth $1,500,000. How muchwas the initial investment:(a)at a simple interest rate of 10% per year?(b)at an interest rate of 10% per year compoundingannually?

Solve the diagram for the unknownQassuming a10% interest rate.

A man borrowed $750 from a bank. He agreed torepay the sum at the end of 3 years, together with theinterest at 8% per year. How much will he owe thebank at the end of 3 years?

We know that a certain piece of equipment will cost$150,000 in 5 years. How much must be depositedtoday using 10% interest to pay for it?

Alvins Uncle Arnold gave him $16,000 from sell-ing the old family farm. Alvin wants to start collegeand have $12,000 available to buy a used car when hegraduates in 4 years. Alvin wants to buy a new com-puter, software,and peripherals now,and he earns 3%in his savings account. How much can he spend onthe computer now and still have enough to grow tothe $12,000 he needs when he graduates?

Suppose that $2000 is deposited in an account thatearns 6% interest. How much is in the account(a)after 5 years?(b)after 10 years?(c)after 20 years?(d)after 50 years?(e)after 100 years?

An inheritance will be $20,000. The interest rate forthe time value of money is 7%. How much is theinheritance worth now, if it will be received(a)in5years?(b)in 10 years?(c)in 20 years?(d)in 50 years?

Rita borrows $5000 from her parents. She repaysthem $6000. What is the interest rate if she pays the$6000 at the end of(a)Year 2?(b)Year 3?(c)Year 5?(d)Year 10?

How long would it take to double your money if youinvest it at 4% simple interest? At 4% compoundinterest?

A savings account earns 8% interest. If $1000 isinvested, how many years is it until each of thefollowing amounts is on deposit?(a)$1360(b)$2720(c)$4316(d)$6848

Mohammed can get a certificate of deposit (CD) athis bank that will pay 3.7% annually for 10 years. Ifhe places$5530in this CD, how much will it beworthwhen it matures?(a)Use the formula.(b)Use the interest tables and interpolation.(c)Use a TVM calculator.

Ace Manufacturing is building a new facility thatwill cost $44M. Ace will borrow $40M from FirstNational Bank and pay the remainder immediatelyas a down payment. Ace will pay 7% interest butwill make no payments for 4 years, at which timethe entire amount will be due. How large will Acespayment be?

How much must you invest now at 7.9% interest toaccumulate $175,000 in 63 years?

a)If $100 at Time 0 will be worth $110 a yearlater and was $90 a year ago, compute the inter-est rate for the past year and the interest rate nextyear.(b)Assume that $90 invested a year ago will return$110 a yearfrom now. What is the annualinterestrate in this situation?

In 1995 an anonymous private collector purchased apainting by Picasso entitledAngel Fernandezde Sotofor $29,152,000. The picture depicts Picassos friendde Soto seated in a Barcelona cafe drinking absinthe.The painting was done in 1903 and was valued thenat $600. If the painting was owned by the same fam-ily until its sale in 1995, what rate of return did theyreceive on the $600 investment?

The following series of payments will repay a presentsum of $5000 at an 8% interest rate. Use single payment factors to find the present sum that is equiv-alent to this series of payments at a 10% interestrate

What sum of money now is equivalent to $8250 twoyears later, if interest is 4% per 6-month period?

A sum of money invested at 2% per 6-month period(semiannually), will double in amount in approxi- mately how many years

One thousand dollars is borrowed for one year atan interest rate of 1% per month. If the same sumof money could be borrowed for the same period atan interest rate of 12% per year, how much could besaved in interest charges?

Sally Stanford is buying a car that costs $12,000.She will pay $2000 immediately and the remaining$10,000 in four annual end-of-year principal pay-ments of $2500 each. In addition to the$2500, shemust pay 15% interest on the unpaid balance of theloan each year. Prepare a cash flow table to representthis situation

The local bank offers to pay 5% interest on savingsdeposits. In a nearby town, the bank pays 1.25% per3-month period (quarterly). A man who has $3000to put in a savings account wonders whether thehigher interest paid in the nearby town justifies driv-ing there to make the deposit. Assuming he will leaveall money in the accountfor 2 years, how much addi-tional interest would he obtain from the out-of-townbank over the local bank

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

The tabulated factors stop atn= 100. How can theybe used to calculate (P/F,i, 150)? (P/F,i, 200)?

In 1990 Mrs. John Hay Whitney sold her paintingby Renoir,Au Moulin de la Galette,depicting a open- air Parisian dance hall, for $71 million. Thebuyer also had to pay the auction house commis-sion of 10%, or a total of $78.1 million. The Whit-ney family had purchased the painting in 1929 for$165,000.(a)What rate of return did Mrs. Whitney receive onthe investment?(b)Was the rate of return really as high as youcomputed in(a)? Explain.

A sumof moneyQwill bereceived 6 yearsfrom now.At 5% annual interest, the present worth ofQis $60.At the same interest rate, what would be the value ofQin 10 years?

A thousand dollars is invested for 7 months at aninterest rate of 1% per month. What is the nomi-nal interest rate? What is the effective interest rate?

A firm charges its credit customers 13/4% interest permonth. What is the effective interest rate?

If the nominal annual interest rate is 12% com-pounded quarterly, what is the effective annualinterest rate?

A local store charges11/2% eachmonth on the unpaidbalance for its charge account. What nominal annualinterest rate is being charged? What is the effectiveinterest rate?

What interest rate, compounded quarterly, isequivalent to a 9.31% effective interest rate?

A bank advertises it pays 7% annual interest, com-pounded daily, on savings accounts, provided themoney is left in the account for 4 years. What is theeffective annual interest rate?

At the Central Furniture Company, customers whobuy on credit pay an effective annual interest rate of16.1%, based on monthly compounding. What is thenominal annual interest rate that they pay?

A student bought a $75 used guitar and agreed topay for it with a single $85 payment at the end of6 months. Assuming semiannual (every 6 months)compounding, what is the nominal annual interestrate? What is the effective interest rate?

A bank is offering to sell 6-month certificates ofdeposit for $9500. At the end of 6 months, the bankwill pay $10,000 to the certificate owner. Based on a6-month interest period, compute the nominal annualinterest rate and the effective annual interest rate

Mr. Sansomewithdrew $1000from a savingsaccountand invested it in common stock. At the end of 5years, he sold the stock and received a check for$1307. If Mr. Sansome had left his $1000 in the sav-ings account, he would have received an interest rateof 5%, compounded quarterly. Mr. Sansome wouldlike to compute a comparable interest rate on hiscommon stock investment. Based on quarterly com-pounding, what nominal annual interest rate did Mr.Sansome receive on his investment in stock? Whateffective annual interest rate did he receive?

The treasurer of a firm noted that many invoices werereceived with the following terms of payment:2%10 days, net 30 days. Thus, if he were to pay the billwithin 10 days of its date, he could deduct 2%. Onthe other hand, if he did not promptly pay the bill, thefull amount would be due 30 days from the date ofthe invoice.Assuminga 20-day compoundingperiod,the 2% deductionfor prompt paymentis equivalenttowhat effective annual interest rate?

Jim Duggan made an investment of $10,000 in asavingsaccount10 yearsago.Thisaccountpaid inter- est of 51/2% for the first 4 years and 61/2% interestfor the remaining 6 years. The interest charges werecompounded quarterly. How much is this investmentworth now?

First Bank is sending alumni of universities an invi-tation to obtain a credit card, with the name of theiruniversity written on it, for a nominal 9.9% interestper year after 6 months of 0% interest. These inter-est rates apply to the outstanding debt if not paid bya specified date each month, and hence interest iscompounded monthly. If you fail to make the mini-mum payment in any month, your interest rate couldincrease (without notice) to a nominal 19.99% peryear. Calculate the effective annual interest rates thecredit company is charging in both cases

Select the best of the following five alternatives.Assume the investment is for a period of 4 years andP=$10,000.A.11.98% interest rate compounded continuouslyB.12.00% interest rate compounded dailyC.12.01% interest rate compounded monthlyD.12.02% interest rate compounded quarterlyE.12.03% interest rate compounded yearly

Traffic at a certain intersection is 2000cars perday.Aconsultant has told the city that traffic is expected togrow at a continuous rate of 5% per year for the next4 years. How much traffic will be expected at the endof 2 years?

A bank pays 10% nominal annual interest on specialthree-year certificates. What is the effective annualinterest rate if interest is compounded(a)Every three months?(b)Daily?(c)Continuously?

A department store charges 13/4% interest per month,compounded continuously, on its customers chargeaccounts. What is the nominal annual interest rate?What is the effective interest rate? (Answers:21%;23.4%)

If you want a 12% rate of return, continuously com-pounded,on a project that will yield $6000 at the endof 21/2years, how much must you be willing to investnow?

Bank North advertises,We pay 6.50%, compoundeddaily. Bank South says, We pay 6.50%, com- pounded continuously. If you deposit $10,000 withBank South for one year, how much additional inter- est will you receive?

Bart wishes to tour the country with his friends. Todo this, he is saving money for a bus.(a)How much money must Bart deposit in a savingsaccountpaying8%nominalannualinterest,com-pounded continuously, in order to have $8000 in41/2years?(b)A friend offers to repay Bart $8000 in 41/2yearsif Bart gives him $5000 now. Assuming contin-uous compounding, what is the nominal annualinterest rate of this offer?

The Ive Been Moved Corporation receives a con-stant flow of funds from its worldwide operations.This money (in the form of checks) is continuouslydeposited in many banks with the goal of earningas much interest as possible for IBM. One billiondollars is deposited each month, and the money earnsan average of1/2% interest per month, compoundedcontinuously. Assume all the money remains in theaccounts until the end of the month.(a)How much interest does IBM earn each month? b)How much interest would IBM earn each monthif it held the checks and made deposits to its bankaccounts just four times a month?

A forklift truck costs $29,000. A company agrees topurchase such a truck with the understanding that itwill make a single payment for the balance due in3 years. The vendor agrees to the deal and offers twodifferent interest schedules. The first schedule usesan annual effective interest rate of 13%. The secondschedule uses 12.75% compounded continuously.(a)Which schedule should the company accept?(b)What would be the size of the single payment?

How long will it take for $10,000, invested at 5% peryear, compounded continuously, to triple in value?

A friend was left $50,000 by his uncle. He hasdecided to put it into a savings account for thenext year or so. He finds there are varying inter-est rates at savings institutions: 43/8% compoundedannually, 41/4% compounded quarterly, and 41/8%compounded continuously. He wishes to select thesavings institution that will give him the highestreturn on his money. What interest rate should heselect?

Jack deposited $500,000 into a bank for 6 months.At the end of that time, he withdrew the money andreceived $520,000. If the bank paid interest based oncontinuous compounding:(a)What was the effective annual interest rate?(b)What was the nominal annual interest rate?

Ace Zenovia Bank and Trust deposits $2,567,223 ofexcess capital in the Federal Reserve Bank. If theFed pays 4% interest compounded daily, how muchinterest will Zenovia earn by leaving the money ondeposit for two years? By how much does assumingcontinuous compounding change the answer?

The U.S. recently purchased $1 billion of 30-yearzero-coupon bonds from a struggling foreign nation.The bonds yield 41/2% per year interest. Thezero-coupon bonds pay no interest during their30-year life. Instead, at the end of 30 years,the U.S. government is to receive back its $1billion together with interest at 41/2% per year. A U.S. senator objected to the purchase, claim-ing that the correct interest rate for bonds likethis is 51/4%. The result, he said, was a multi-million dollar gift to the foreign country withoutthe approval of Congress. Assuming the senatorsmath is correct, how much will the foreign countryhave saved in interest when it repays the bonds at41/2% instead of 51/4% at the end of 30 years?

The Apex Company sold a water softener to MartySmith. The price of the unit was $350. Marty askedfor a deferred payment plan, and a contract was writ-ten. Under the contract, the buyer could delay payingfor the water softener if he purchased the coarse saltfor recharging the softener from Apex. At the end of2 years, the buyer was to pay for the unit in a lumpsum, with interest at a rate of 1.5% per quarter-year.According to the contract, if the customer ceasedbuying salt from Apex at any time prior to 2 years,the full payment due at the end of 2 years wouldautomatically become due.Six months later, Marty decided to buy saltelsewhere and stopped buying from Apex, where-upon Apex asked for the full payment that was tohave been due 18 months hence. Marty was unhappyabout this, so Apex offered as an alternative to acceptthe $350 with interest at 10% per semiannual periodfor the 6 months that Marty had been buying saltfrom Apex. Which of these alternatives should Martyaccept? Explain.

The local garbage company charges $6 a monthfor garbage collection. It had been their practiceto send out bills to their100,000 customers at theend of each 2-month period. Thus, at the end ofFebruary it would send a bill to each customerfor $12 for garbage collection during January andFebruary.Recently the firm changed its billing date: itnow sends out the 2-month bills after one monthsservice has been performed. Bills for January andFebruary, for example, are sent out at the end ofJanuary. The local newspaper points out that the firmis receiving half its money before the garbage collec-tion. This unearnedmoney,the newspapersays,couldbe temporarily invested for one month at 1% permonth interest by the garbage company to earn extraincome.Compute how much extra income the garbagecompany could earn each year if it invests the moneyas described by the newspaper.