123446472 Time Value of Money Test Banks

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CHAPTER 2

TIME VALUE OF MONEY

(Difficulty: E = Easy M = M!"iu# a$" T = T%u&'

Note: Most problems assume students have a calculator with a yx feature(i.e., an exponential feature). Annuity problems for finding the interestrate or the number of periods are in the financial calculator section at theend of this chapter.

Multi)l! C'%ic!: C%$c!)tual

Easy:

PV and discount rate Answer: a Diff: E1. You have determined the profitability of a planned proect by finding

the present value of all the cash flows from that proect. !hich of

the following would cause the proect to loo" more appealing in termsof the present value of those cash flows#

a. $he discount rate decreases.b. $he cash flows are extended over a longer period of time, but the

total amount of the cash flows remains the same.c. $he discount rate increases.d. Answers b and c above.e. Answers a and b above.

PV versus FV Answer: e Diff: E%. !hich of the following statements is most correct#

a. &f the discount (or interest) rate is positive, the future value ofan expected series of payments will always exceed the present valueof the same series.

b. $o increase present consumption beyond present income normallyre'uires either the payment of interest or else an opportunity costof interest foregone.

c. isregarding ris", if money has time value, it is impossible for thepresent value of a given sum to be greater than its future value.

d. isregarding ris", if the present value of a sum is e'ual to itsfuture value, either " * or t *.

e. +ach of the statements above is true.

Time value concepts Answer: e Diff: E

. !hich of the following statements is most correct#

a. A -year /1** annuity due will have a higher present value than a -year /1** ordinary annuity.

b. A 1-year mortgage will have larger monthly payments than a *yearmortgage of the same amount and same interest rate.

c. &f an investment pays 1* percent interest compounded annually, itseffective rate will also be 1* percent.

Chapter 2 - Page 1



d. 0tatements a and c are correct.e. All of the statements above are correct.

Time value concepts Answer: d Diff: E

. $he future value of a lump sum at the end of five years is /1,***. $henominal interest rate is 1* percent and interest is compoundedsemiannually. !hich of the following statements is most correct#

a. $he present value of the /1,*** is greater if interest is compoundedmonthly rather than semiannually.

b. $he effective annual rate is greater than 1* percent.c. $he periodic interest rate is - percent.d. 2oth statements b and c are correct.e. All of the statements above are correct.

Time value concepts Answer: d Diff: E-. !hich of the following statements is most correct#

a. $he present value of an annuity due will exceed the present value ofan ordinary annuity (assuming all else e'ual).b. $he future value of an annuity due will exceed the future value of

an ordinary annuity (assuming all else e'ual).c. $he nominal interest rate will always be greater than or e'ual to

the effective annual interest rate.d. 0tatements a and b are correct.e. All of the statements above are correct.

Effective annual rate Answer: d Diff: E3. !hich of the following statements is most correct#

a. &f annual compounding is used, the effective annual rate e'uals thenominal rate.

b. &f annual compounding is used, the effective annual rate e'uals theperiodic rate.

c. &f a loan has a 1% percent nominal rate with semiannual compounding,its effective annual rate is e'ual to 11.33 percent.

d. Answers a and b are correct.e. Answers a and c are correct.

Chapter 2 - Page 2



Effective annual rate Answer: b Diff: E4. !hich of the following ban" accounts has the highest effective annual

return#

a. An account which pays 1* percent nominal interest with monthly compounding.

b. An account which pays 1* percent nominal interest with daily compounding.

c. An account which pays 1* percent nominal interest with annual compounding.

d. An account which pays 5 percent nominal interest with daily compounding.

e. All of the investments above have the same effective annual return.

Effective annual rate Answer: d Diff: E6. You are interested in investing your money in a ban" account. !hich of

the following ban"s provides you with the highest effective rate ofinterest#

a. 2an" 17 6 percent with monthly compounding.

b. 2an" %7 6 percent with annual compounding.c. 2an" 7 6 percent with 'uarterly compounding.d. 2an" 7 6 percent with daily (3-day) compounding.e. 2an" -7 4.6 percent with annual compounding.

Amortization Answer: b Diff: E5. Your family recently obtained a *year (3*month) /1**,*** fixedrate

mortgage. !hich of the following statements is most correct# (&gnoreall taxes and transactions costs.)

a. $he remaining balance after three years will be /1**,*** less thetotal amount of interest paid during the first 3 months.

b. $he proportion of the monthly payment that goes towards repayment ofprincipal will be higher ten years from now than it will be thisyear.

c. $he monthly payment on the mortgage will steadily decline over time.d. All of the statements above are correct.

e. 8one of the statements above is correct.

Chapter 2 - Page 3



Amortization Answer: e Diff: E1*. 9ran" :ewis has a *year, /1**,*** mortgage with a nominal interest

rate of 1* percent and monthly compounding. !hich of the followingstatements regarding his mortgage is most correct#

a. $he monthly payments will decline over time.b. $he proportion of the monthly payment which represents interest will

be lower for the last payment than for the first payment on the loan.c. $he total dollar amount of principal being paid off each month gets

larger as the loan approaches maturity.d. 0tatements a and c are correct.e. 0tatements b and c are correct.

Medium:

Annuities Answer: c Diff: M 11. 0uppose someone offered you the choice of two e'ually ris"y annuities,

each paying /1*,*** per year for five years. ;ne is an ordinary (ordeferred) annuity, the other is an annuity due. !hich of the following

statements is most correct#

a. $he present value of the ordinary annuity must exceed the presentvalue of the annuity due, but the future value of an ordinaryannuity may be less than the future value of the annuity due.

b. $he present value of the annuity due exceeds the present value ofthe ordinary annuity, while the future value of the annuity due isless than the future value of the ordinary annuity.

c. $he present value of the annuity due exceeds the present value ofthe ordinary annuity, and the future value of the annuity due alsoexceeds the future value of the ordinary annuity.

d. &f interest rates increase, the difference between the present valueof the ordinary annuity and the present value of the annuity due

remains the same.e. Answers a and d are correct.

Chapter 2 - Page 4



Time value concepts Answer: e Diff: M 1%. A /1*,*** loan is to be amorti<ed over - years, with annual endofyear

payments. =iven the following facts, which of these statements is mostcorrect#

a. $he annual payments would be larger if the interest rate were lower.b. &f the loan were amorti<ed over 1* years rather than - years, and if

the interest rate were the same in either case, the first paymentwould include more dollars of interest under the -year amorti<ationplan.

c. $he last payment would have a higher proportion of interest than thefirst payment.

d. $he proportion of interest versus principal repayment would be thesame for each of the - payments.

e. $he proportion of each payment that represents interest as opposedto repayment of principal would be higher if the interest rate werehigher.

Time value concepts Answer: e Diff: M 1. !hich of the following is most correct#

a. $he present value of a -year annuity due will exceed the presentvalue of a -year ordinary annuity. (Assume that both annuities pay/1** per period and there is no chance of default.)

b. &f a loan has a nominal rate of 1* percent, then the effective ratecan never be less than 1* percent.

c. &f there is annual compounding, then the effective, periodic, andnominal rates of interest are all the same.

d. Answers a and c are correct.e. All of the answers above are correct.

Time value concepts Answer: c Diff: M 1. !hich of the following statements is most correct#

a. An investment which compounds interest semiannually, and has anominal rate of 1* percent, will have an effective rate less than 1*percent.

b. $he present value of a threeyear /1** annuity due is less than thepresent value of a threeyear /1** ordinary annuity.

c. $he proportion of the payment of a fully amorti<ed loan which goestoward interest declines over time.

d. 0tatements a and c are correct.e. 8one of the answers above is correct.

Chapter 2 - Page 5



Tough:

Time value concepts Answer: d Diff: T1-. !hich of the following statements is most correct#

a. $he first payment under a year, annual payment, amorti<ed loan for

/1,*** will include asmaller

percentage (or fraction) of interestif the interest rate is - percent than if it is 1* percent.b. &f you are lending money, then, based on effective interest rates,

you should prefer to lend at a 1* percent nominal, or 'uoted, ratebut with semiannual payments, rather than at a 1*.1 percent nominalrate with annual payments. >owever, as a borrower you should preferthe annual payment loan.

c. $he value of a perpetuity (say for /1** per year) will approachinfinity as the interest rate used to evaluate the perpetuityapproaches <ero.

d. 0tatements a, b, and c are all true.e. 0tatements b and c are true.

Multi)l! C'%ic!: P*%+l!#s

Easy:

Solving for for an annuit! Answer: b Diff: E

13. You are currently investing your money in a ban" account which has anominal annual rate of 5 percent, compounded monthly. &f you invest/5** at the end of each month, how many months will it ta"e for youraccount to grow to /*1,*33.%4 (rounded to the nearest month)#

a. * monthsb. 136 monthsc. 14- monthsd. %%1 monthse. - months

ominal and effective rates Answer: b Diff: E14. An investment pays you 5 percent interest compounded semiannually. A

second investment of e'ual ris", pays interest compounded 'uarterly.!hat nominal rate of interest would you have to receive on the secondinvestment in order to ma"e you indifferent between the two investments#

a. 6.41?

b. 6.5*?c. 5.**?d. 5.%*?e. 5.1?

Effective annual rate Answer: c Diff: E16. You want to borrow /1,*** from a friend for one year, and you propose

to pay her /1,1%* at the end of the year. 0he agrees to lend you the

Chapter 2 - Page 6



/1,***, but she wants you to pay her /1* of interest at the end of eachof the first 11 months plus /1,*1* at the end of the 1%th month. >owmuch higher is the effective annual rate under your friend@s proposalthan under your proposal#

a. *.**?b. *.-?c. *.36?d. *.65?e. 1.**?

Time for a sum to double Answer: d Diff: E15. You are currently investing your money in a ban" account which has a

nominal annual rate of 4 percent, compounded monthly. >ow many yearswill it ta"e for you to double your money#

a. 6.34 yearsb. 5.1- years

c. 5.-* yearsd. 5.5 yearse. 1*.%- years

Mont"l! pa!ments on loan Answer: c Diff: E%*. You are considering buying a new car. $he stic"er price is /1-,*** and

you have /%,*** to put toward a down payment. &f you can negotiate anominal annual interest rate of 1* percent and you wish to pay for thecar over a -year period, what are your monthly car payments#

a. /%13.34b. /%-%.c. /%43.%1d. /%6-.46e. /16.41

#nterest rate of an annuit! Answer: b Diff: E%1. 0outh enn $ruc"ing is financing a new truc" with a loan of /1*,*** to

be repaid in - annual endofyear installments of /%,-*.-3. !hatannual interest rate is the company paying#

a. 4?b. 6?c. 5?d. 1*?e. 11?

Medium:

Chapter 2 - Page 7



Effective annual rate Answer: b Diff: M %%. &f it were evaluated with an interest rate of * percent, a 1*year

regular annuity would have a present value of /,4--.-*. &f the future

(compounded) value of this annuity, evaluated at Year 1*, is /-,*.%%,what effective annual interest rate must the analyst be using to findthe future value#

a. 4?b. 6?c. 5?d. 1*?e. 11?

FV of a sum Answer: d Diff: M %. 0uppose you put /1** into a savings account today, the account pays a

nominal annual interest rate of 3 percent, but compounded semiannually,and you withdraw /1** after 3 months. !hat would your ending balancebe %* years after the initial /1** deposit was made#

a. /%%3.%*b. /11-.-c. / 3%.51d. / 5.-*e. / .**

FV of annuit! due Answer: d Diff: M %. You are contributing money to an investment account so that you can

purchase a house in five years. You plan to contribute six payments of/,*** a yearthe first payment will be made today (t *), and thefinal payment will be made five years from now (t -). &f you earn 11percent in your investment account, how much money will you have in theaccount five years from now (at t -)#

a. /15,1%b. /%*,6-3c. /%1,36d. /%,45e. /%3,-*

Chapter 2 - Page 8



Effective annual rate Answer: a Diff: M %-. You have ust borrowed /%*,*** to buy a new car. $he loan agreement

calls for 3* monthly payments of /.65 each to begin one month fromtoday. &f the interest is compounded monthly, then what is theeffective annual rate on this loan#

a. 1%.36?b. 1.1%?c. 1%.**?d. 1.%-?e. 1-.*6?

Effective annual rate Answer: e Diff: M %3. You have ust ta"en out a 1*year, /1%,*** loan to purchase a new car.

$his loan is to be repaid in 1%* e'ual endofmonth installments. &feach of the monthly installments is /1-*, what is the effective annualinterest rate on this car loan#

a. 3.-1?

b. 4.65%?c. 6.365%?d. 6.6635?e. 5.*6?

PV and non$annual discounting Answer: b Diff: M %4. Your lease calls for payments of /-** at the end of each month for the

next 1% months. 8ow your landlord offers you a new 1year lease whichcalls for <ero rent for months, then rental payments of /4** at theend of each month for the next 5 months. You "eep your money in a ban"time deposit that pays a nominal annual rate of - percent. 2y whatamount would your net worth change if you accept the new lease# (>intBYour return per month is -?C1% *.133334?.)

a. /-*5.61b. /%-.3%c. D/1%-.*d. D/%-.3%e. D/-*5.61

Chapter 2 - Page 9



FV under mont"l! compounding Answer: d Diff: M %6. 0teven ust deposited /1*,*** in a ban" account which has a 1% percent

nominal interest rate, and the interest is compounded monthly. 0tevenalso plans to contribute another /1*,*** to the account one year (1%months) from now and another /%*,*** to the account two years from now.>ow much will be in the account three years (3 months) from now#

a. /-4,%1b. /6,55c. /-*,541d. /5,-%e. /5,1*

FV under dail! compounding Answer: a Diff: M %5. You have /%,*** invested in a ban" account that pays a percent

nominal annual interest with daily compounding. >ow much money willyou have in the account at the end of Euly (i.e., in 1% days)#(Assume there are 3- days in each year.)

a. /%,*%5.1

b. /%,*%6.5c. /%,**.**d. /%,*%.e. /%,*%.55

PV under mont"l! compounding Answer: b Diff: M *. You have ust bought a security which pays /-** every six months. $he

security lasts for ten years. Another security of e'ual ris" also hasa maturity of ten years, and pays 1* percent compounded monthly (thatis, the nominal rate is 1* percent). !hat should be the price of thesecurity that you ust purchased#

a. /3,1*6.3b. /3,14-.6%c. /3,%1.11d. /3,-33.%1e. /4,1.63

PV under non$annual compounding Answer: c Diff: M 1. You have been offered an investment that pays /-** at the end of every

3 months for the next years. $he nominal interest rate is 1%percent7 however, interest is compounded 'uarterly. !hat is thepresent value of the investment#

a. /%,-6.33b. /%,.34

c. /%,-1.4d. /%,3.e. /%,4.-3

Value of missing pa!ments Answer: d Diff: M %. You recently purchased a %*year investment which pays you /1** at

t 1, /-** at t %, /4-* at t , and some fixed cash flow, F, atthe end of each of the remaining 14 years. $he investment cost you

Chapter 2 - Page 10



/-,-.64. Alternative investments of e'ual ris" have a re'uired returnof 5 percent. !hat is the annual cash flow received at the end of eachof the final 14 years, that is, what is F#

a. /3**b. /3%-c. /3-*d. /34-e. /4**

Value of missing pa!ments Answer: c Diff: M . A tenyear security generates cash flows of /%,*** a year at the end of

each of the next three years (t 1, %, ). After three years, thesecurity pays some constant cash flow at the end of each of the nextsix years. (t , -, 3, 4, 6, 5). $en years from now (t 1*) thesecurity will mature and pay /1*,***. $he security sells for/%,*4.6-, and has a yield to maturity of 4. percent. !hat annualcash flow does the security pay for years through 5#

a. /%,55-

b. /,-36c. /,4**d. /,54*e. /,%53

Value of missing pa!ments Answer: d Diff: M . An investment costs /,*** today and provides cash flows at the end of

each year for %* years. $he investmentGs expected return is 1*percent. $he proected cash flows for years 1, %, and are /1**, /%**,and /** respectively. !hat is the annual cash flow received for eachof the years through %* (14 years)# (Assume the same payment foreach of these years.)

a. /%6-.1b. /1.53c. /45.65d. /14.64e. /-5.33

Amortization Answer: d Diff: M -. You have ust bought a house and have a /1%-,***, %-year mortgage with

a fixed interest rate of 6.- percent with monthly payments. ;ver thenext five years, what percentage of your mortgage payments will gotoward the repayment of principal#

a. 6.-*?b. 1*.34?

c. 1%.66?d. 1.5?e. 14.--?

Amortization Answer: a Diff: M 3. You have ust ta"en out an installment loan for /1**,***. Assume that

the loan will be repaid in 1% e'ual monthly installments of /5,-3 andthat the first payment will be due one month from today. >ow much of

Chapter 2 - Page 11



your third monthly payment will go toward the repayment of principal#

a. /4,4-4.13b. /3,-5.1%c. /4,%1%.-*d. /4,5%-.66e. /6,.

Amortization Answer: c Diff: M 4. A homeowner ust obtained a /5*,*** mortgage. $he mortgage is for *

years (3* months) and has a fixed nominal annual rate of 5 percent,with monthly payments. !hat percentage of the total payments made thefirst two years will go toward repayment of interest#

a. 65.*?b. 51.4*?c. 5%.-5?d. 5.3-?e. 5.43?

%emaining balance on mortgage Answer: d Diff: M 6. Your family purchased a house three years ago. !hen you bought the

house you financed it with a /13*,*** mortgage with an 6.- percentnominal interest rate (compounded monthly). $he mortgage was for 1-years (16* months). !hat is the remaining balance on your mortgagetoday#

a. / 5-,35b. /1*,**c. /1%-,4-d. /11,54e. /1-5,556

Tough:

%e&uired annuit! pa!ments Answer: d Diff: T5. Your father, who is 3*, plans to retire in % years, and he expects to

live independently for years. 0uppose your father wants to have areal income of /*,*** in today@s dollars in each year after heretires. >is retirement income will start the day he retires, % yearsfrom today, and he will receive a total of retirement payments.

&nflation is expected to be constant at - percent. Your father has/1**,*** in savings now, and he can earn 6 percent on savings now andin the future. >ow much must he save each year, starting today , to meethis retirement goals#

a. /1,63b. /%,*c. /%,413d. /-,-*e. /3,1*%

Chapter 2 - Page 12



%e&uired annuit! pa!ments Answer: a Diff: T*. Your client ust turned 4- years old and plans on retiring in 1* years

on her 6-th birthday. 0he is saving money today for her retirement andis establishing a retirement account with your office. 0he would li"eto withdraw money from her retirement account on her birthday each yearuntil she dies. 0he would ideally li"e to withdraw /-*,*** on her 6-thbirthday, and increase her withdrawals 1* percent a year through her65th birthday (i.e., she would li"e to withdraw /4,%*- on her 65thbirthday). 0he plans to die on her 5*th birthday, at which time shewould li"e to leave /%**,*** to her descendants. Your client currentlyhas /1**,***. You estimate that the money in the retirement accountwill earn 6 percent a year over the next 1- years.

Your client plans to contribute an e'ual amount of money each yearuntil her retirement. >er first contribution will come in 1 year7 her1*th and final contribution will come in 1* years (on her 6-thbirthday). >ow much should she contribute each year to meet herobectives#

a. /1%,*1.-5

b. /1%,556.3c. /1,%.16d. /1,4-5.e. /1,*%1.-

Chapter 2 - Page 13



%e&uired annuit! pa!ments Answer: c Diff: T1. You are considering an investment in a *year security. $he security

will pay /%- a year at the end of each of the first three years. $hesecurity will then pay /* a year at the end of each of the next %*years. $he nominal interest rate is assumed to be 6 percent, and thecurrent price (present value) of the security is /3*.5. =iven thisinformation, what is the e'ual annual payment to be received from Year% through Year * (i.e., for 14 years)#

a. /-b. /6c. /*d. /-e. /-*

%e&uired annuit! pa!ments Answer: a Diff: T%. Eoe and Eane are interested in saving money to put their two children,

Eohn and 0usy through college. Eohn is currently 1% years old and willenter college in six years. 0usy is 1* years old and will entercollege in 6 years. 2oth children plan to finish college in four years.

Hollege costs are currently /1-,*** a year (per child), and areexpected to increase at - percent a year for the foreseeable future.All college costs are paid at the beginning of the school year. Ipuntil now, Eoe and Eane have saved nothing but they expect to receive/%-,*** from a favorite uncle in three years.

$o provide for the additional funds that are needed, they expect toma"e 1% e'ual payments at the beginning of each of the next twelveyearsthe first payment will be made today and the final payment willbe made on 0usyGs %1st birthday (which is also the day that the lastpayment must be made to the college). &f all funds are invested in astoc" fund which is expected to earn 1% percent, how large should eachof the annual contributions be#

a. / 4,4-.3*b. / 4,456.43c. / 6,4%.34d. / 5,34-.56e. /1,41.5*

Chapter 2 - Page 14



%e&uired annuit! pa!ments Answer: b

Diff: T

. Eim and 8ancy are interested in saving money for their son@s education.$oday is their son@s 6th birthday. $heir son will enter college tenyears from now on his 16th birthday, and will attend for four years.All college costs are due at the beginning of the year, so Eim and8ancy will have to ma"e payments on their son@s 16th, 15th, %*th and%1st birthdays (t 1*, 11, 1%, 1). $hey estimate that the collegetheir son wants to attend will cost /-,*** the first year (t 1*) andthat the costs will increase 4 percent each year (the final collegepayment will be made 1 years from now).

Hurrently, Eim and 8ancy have /%*,*** in an investment account. $heyalso plan to contribute a fixed amount at the end of each of the nextten years (t 1, %, , ... 1*). $heir invested money will be in anaccount which pays 5 percent interest compounded annually. >ow muchmoney do Eim and 8ancy need to contribute to the account in each of thenext ten years#

a. /-,36b. /-,66c. /3,*-%d. /3,6-e. /4,%6-

FV of annuit! due Answer: a Diff: T. $o save money for a new house, you want to begin contributing money to

a bro"erage account. Your plan is to ma"e ten contributions to thebro"erage account. +ach contribution will be for /1,-**. $he contributions will come at the beginning of each of the next 1* years,i.e., the first contribution will be made at t * and the finalcontribution will be made at t 5. Assume that the bro"erage accountpays a 5 percent return with 'uarterly compounding. >ow much money doyou expect to have in the bro"erage account nine years from now (t 5)#

a. /%,1%4.5b. /%-,1*.3-c. /%-,%6*.%4d. /%1,3%4.5e. /15,46-.43

FV of investment account Answer: b Diff: T-. Jelly and 2rian Eohnson are a recently married couple whose parents

have counseled them to start saving immediately in order to have enoughmoney down the road to pay for their retirement and their childrenGs

college expenses. $oday (t *) is their %-th birthday (the coupleshares the same birthday).

$he couple plans to have two children (ic" and Eane). ic" isexpected to enter college %* years from now (t %*)7 Eane is expectedto enter college %% years from now (t %%). 0o in years t %% and t % there will be two children in college. +ach child will ta"e years to complete college, and college costs are paid at the beginning

Chapter 2 - Page 15



of each year of college.

Hollege costs per child will be as followsB

Year Host per child Hhildren in college %* / -6,*- ic" %1 / 3%,1*6 ic"

%% / 33,-3 ic" and Eane % / 41,1*6 ic" and Eane % / 43,*63 Eane %- / 61,11 Eane

Jelly and 2rian plan to retire forty years from now at age 3- (att *). $hey plan to contribute /1%,*** per year at the end of eachyear for the next * years into an investment account that earns 1*percent per year. $his account will be used to pay for the collegecosts, and also to provide a nest egg for Jelly and 2rianGs retirementat age 3-. >ow big will Jelly and 2rianGs nest egg (the balance of theinvestment account) be when they retire at age 3- (t *)#

a. /1,6-,3%b. /%,5,%4c. /%,3-6,-1d. /,-3,4-1e. /,4-6,

Effective annual rate Answer: c Diff: T3. You have some money on deposit in a ban" account which pays a nominal

(or 'uoted) rate of 6.*5 percent, but with interest compounded daily(using a 3-day year). Your friend owns a security which calls forthe payment of /1*,*** after %4 months. $he security is ust as safeas your ban" deposit, and your friend offers to sell it to you for/6,***. &f you buy the security, by how much will the effective annualrate of return on your investment change#

a. 1.64?b. 1.-?c. %.**?d. *.53?e. *.?

on$annual compounding Answer: a Diff: T4. A financial planner has offered you three possible options for

receiving cash flows. You must choose the option that has the highestpresent value.

(1) /1,*** now and another /1,*** at the beginning of each of the 11

subse'uent months during the remainder of the year, to bedeposited in an account paying a 1% percent nominal annual rate,but compounded monthly (to be left on deposit for the year).

(%) /1%,4-* at the end of the year (assume a 1% percent nominalinterest rate with semiannual compounding).

() A payment scheme of 6 'uarterly payments made over the next twoyears. $he first payment of /6** is to be made at the end of thecurrent 'uarter. ayments will increase by %* percent each

Chapter 2 - Page 16



'uarter. $he money is to be deposited in an account paying a 1%percent nominal annual rate, but compounded 'uarterly (to be lefton deposit for the entire %year period).

!hich one would you choose#

a. Hhoice 1.b. Hhoice %.c. Hhoice .d. Any one, since they all have the same present value.e. Hhoice 1, if the payments were made at the end of each month.

PMT and &uarterl! compounding Answer: b Diff: T6. Your employer has agreed to ma"e 6* 'uarterly payments of /** each

into a trust account to fund your early retirement. $he first paymentwill be made months from now. At the end of %* years (6* payments),you will be paid 1* e'ual annual payments, with the first payment to bemade at the beginning of Year %1 (or the end of Year %*). $he fundswill be invested at a nominal rate of 6 percent, 'uarterly compounding,during both the accumulation and the distribution periods. >ow large

will each of your 1* receipts be# (>intB You must find the +AK and useit in one of your calculations.)

a. / 4,-31b. /1*,465c. /11,346d. /1%,%e. /1,115

PV of an uneven 'F stream Answer: d Diff: T5. >illary is trying to determine the cost of health care to college

students, and parents@ ability to cover those costs. 0he assumes thatthe cost of one year of health care for a college student is /1,***today, that the average student is 16 when he or she enters college,that inflation in health care cost is rising at the rate of 1* percentper year, and that parents can save /1** per year to help cover theirchildren@s costs. All payments occur at the end of the relevantperiod, and the /1**Cyear savings will stop the day the child enterscollege (hence 16 payments will be made). 0avings can be invested at anominal rate of 3 percent, annual compounding. >illary wants a healthcare plan which covers the fully inflated cost of health care for astudent for years, during Years 15 through %% (with payments made atthe end of years 15 through %%). >ow much would the government have toset aside now (when a child is born), to supplement the averageparent@s share of a child@s college health care cost# $he lump sum thegovernment sets aside will also be invested at 3 percent, annualcompounding.

a. /1,*6%.43b. /,554.61c. /-,34.%d. /4,4%.*6e. /6,--.6

Chapter 2 - Page 17



CHAPTER 2

AN,-ER, AND ,OLUTION,

Chapter 2 - Page 18



1( PV and discount rate Answer: a Diff: E

%( PV versus FV Answer: e Diff: E

( Time value concepts Answer: e Diff: E

( Time value concepts Answer: d Diff: E

0tatements b and c are correct7 therefore, statement d is the correct choice.$he present value is smaller if interest is compounded monthly rather thansemiannually.

-( Time value concepts Answer: d Diff: E

0tatements a and b are correct7 therefore, statement d is the correct choice.$he nominal interest rate will be less than the effective rate when thenumber of periods per year is greater than one.

33

( Effective annual rate Answer: d Diff: E

0tatement d is correct. $he e'uation for +AK is as followsB+AK 1

m

r 1

m

Nom −

+

&f annual compounding is used, m 1 and the e'uation above reduces to +AK r8om. $he e'uation for the periodic rate isB

mr

r Nom

PER = .

&f annual compounding is used then m 1 and r +K r8om, and since +AK r8om

then r+K +AK.

4( Effective annual rate Answer: b Diff: E

$he ban" account which pays the highest nominal rate with the most fre'uentrate of compounding will have the highest +AK. Honse'uently, statement b isthe correct choice.

6( Effective annual rate Answer: d Diff: E

0tatement d is correct7 the other statements are incorrect. :oo"ing atresponses a through d, you should reali<e the choice with the greatestfre'uency of compounding will give you the highest +AK. $his is statement d.8ow, compare choices d and e. !e "now +AKd L 4.6?7 therefore, statement d isthe correct choice. $he +AK of each of the statements is shown below.

+AKa 6.*?7 +AKb 6?7 +AKc 6.%?7 +AKd 6.%6?7 +AKe 4.6?.

5( Amortization Answer: b Diff: E

0tatement b is true7 the others are false. $he remaining balance after threeyears will be /1**,*** less the total amount of repaid principal during thefirst 3 months. ;n a fixedrate mortgage the monthly payment remains thesame.

1*( Amortization Answer: e Diff: E



0tatements b and c are correct7 therefore, statement e is the correct choice.Monthly payments will remain the same over the life of the loan.

11( Annuities Answer: c Diff: M

2y definition, an annuity due is received at the beginning of the year whilean ordinary annuity is received at the end of the year. 2ecause the paymentsare received earlier, both the present and future values of the annuity due

are greater than those of the ordinary annuity.

1%( Time value concepts Answer: e Diff: M

&f the interest rate were higher, the payments would all be higher, and allof the increase would be attributable to interest. 0o, the proportion ofeach payment that represents interest would be higher. 8ote that statement bis false because interest during Year 1 would be the interest rate times thebeginning balance, which is /1*,***. !ith the same interest rate and thesame beginning balance, the Year 1 interest charge will be the same,regardless of whether the loan is amorti<ed over - or 1* years.

1( Time value concepts Answer: e Diff: M

1( Time value concepts Answer: c Diff: M

0tatement c is correct7 the other statements are false. $he effective rateof the investment in statement a is 1*.%-?. $he present value of the annuitydue is greater than the present value of the ordinary annuity.

1-1( Time value concepts Answer: d Diff: T

13( Solving for for a single pa!ment Answer: b Diff: E

9inancial calculator solutionB

* 9 *1,*33.%4 M$ 5** & 5C1% *.4- 8 # 136 months.

14

( ominal and effective rates Answer: b Diff: E

1st investment +nter the followingB 8;M? 5 CYK % 0olve for +99? 5.%*%-?.

%nd investment +nter the followingB +99? 5.%*%- CYK 0olve for 8;M? 6.5*?.

16



( Effective annual rate Answer: c Diff: E

Your proposalB+AK1 /1%*C/1,***+AK1 1%?.

Your friend@s proposalB

&nterest is being paid each month (/1*C/1,*** 1? per month), so itcompounds, and the +AK is higher than r8om 1%?B

+AK%

1%

*.1% D1

1%

1 1%.36?.

ifference 1%.36? 1%.**? *.36?.

You could also visuali<e your friend@s proposal in a time line formatB

* i# 1 % 11 1%

NOOOOOOOOOOOOONOOOOOOOOOOOONOOOO . . . OOONOOOOOOOOOOOON

1,*** 1* 1* 1* 1,*1*

&nsert those cash flows in the cash flow register of a calculator and solvefor &KK. $he answer is 1?, but this is a monthly rate. $he nominal rate is1%(1?) 1%?, which converts to an +AK of 1%.36? as followsB&nput into a financial calculator the followingBCYK 1%, 8;M? 1%, and solve for +99? 1%.36?.

15( Time for a sum to double Answer: d Diff: E

1 9 % M$ * & 4C1% 8 # 115.14 months 5.5 years.

%*%( Mont"l! pa!ments on loan Answer: c Diff: E

9irst, find the monthly interest rate *.1*C1% *.6?Cmonth. 8ow, enterin your calculator 8 3*, &CYK *.6, 1,***, 9 *, and solve forM$ /%43.%1.

%1%( #nterest rate of an annuit! Answer: b Diff: E

$ime :ineB* i # 1 % - Years

NOOOOOOOOOOONOOOOOOOOOOOONOOOOOOOOOOOONOOOOOOOOOOOONOOOOOOOOOOOON1*,*** %,-*.-3 %,-*.-3 %,-*.-3 %,-*.-3 %,-*.-3

$abular solutionB

/1*,*** /%,-*.-3(&9Ai,-)&9Ai,- /1*,***C/%,-*.-3 .55%4 i 6?.

9inancial calculator solutionB&nputsB 8 -7 1*,***7 M$ %,-*.-37 9 *. ;utputB & 6?.

%%%( Effective annual rate Answer: b Diff: M



$ime :ineB

i2 ) #

* iA ) *? 1 % 1* Years

P P P P P . . . P

) ,4--.-* M$ M$ M$ M$ M$

M$2 ) M$A ) 4-.-- 9 ) -,*.%%

9inancial calculator solutionBCalculate the PMT of the annuity &nputsB 8 1*7 & *7 ,4--.-*7 9 *. ;utputB M$ /4-.--.Calculate the effective annual interest rate&nputsB 8 1*7 *7 M$ 4-.--7 9 -,*.%%.;utputB & 4.555 ≈ 6.*?.

%%

( FV of a sum Answer: d Diff: M

$ime :ineB* ? 1 % * 3months

P P P P P ... P eriods

1** 1** 9 ) #

$abularC8umerical solutionBSolve for amount on deposit at the end of 6 months

0tep 1 9 /1**(9&9?,1) /1** /.**.9 /1**(1 D *.*3C%) /1** /.**.

0tep % Compound the !"## for "$ periods at "%

9 /.**(9&9?,5) /5.-*.0ince table does not show 5 periods, use numericalCcalculatorexponent method.

9 /.**(1.*)5

/5.-*.9inancial calculator solutionB (0tep % only)&nputsB 8 57 & 7 .**7 M$ *. ;utputB 9 /5.-*.

%( FV of annuit! due Answer: d Diff: M

$here are a few ways to do this. ;ne way is shown below.$o get the value at t - of the first - paymentsB2+=&8 mode8 -& 11 *M$ ,***

9 /%*,46.-6

8ow add on to this the last payment that occurs at t -./%*,46.-6 D /,*** /%,46.-6 ≈ /%,45.

%-



%

( Effective annual rate Answer: a Diff: M

$ime :ineB

+AK ) #* i ) # 1 % 3* Months

P P P ... P

) %*,*** .65 .65 .65

$abular solutionB/%*,*** /.65(&9Ai,3*)&9Ai,3* .5-5

i 1?.+AK (1.*1)1% 1.* 1.1%361 1.* *.1%36 1%.36?.

9inancial calculator solutionBCalculate periodic rate and nominal rate

&nputsB 8 3*7 %*,***7 M$ .657 9 *.;utputB & 1.*. 8;M? 1.*? × 1% 1%.**?.&se interest rate conversion feature

&nputsB CYK 1%7 8;M? 1%.*. ;utputB +99? +AK 1%.36?.

%3( Effective annual rate Answer: e Diff: M

=ivenB :oan alue /1%,***7 :oan $erm 1* years (1%* months)7Monthly ayment /1-*.

8 1%* 1%,***M$ 1-*9 *

0olve for &CYK *.4%1 × 1% 6.365%?. >owever, this is a nominal rate.$o find the effective rate, enter the followingB8;M? 6.365%CYK 1%0olve for +99? 5.*6?.

%4%

( PV and non$annual discounting Answer: b Diff: M

Hurrent * -?C1% *.134? 1 % 1%lease P P P P . . . P

* -** -** -** -**

- C 1 % )

1 % * . 1 3 4 - * *

- , 6 * . 3 1

8 & A A M $ 9



8ew *-?C1% *.134? 1 % 1%

lease P P P P P P

* * * * 4** 4*

H9* * H91 *H91% 4** & *.1340olve for 8 /3,*5.%.

$herefore, the of payments under the proposed lease would be greater thanthe of payments under the old lease by /3,*5.% /-,6*.31 /%-.3%.$hus, your net worth would decrease by /%-.3%.

%6( FV under mont"l! compounding Answer: d Diff: M

0tep 1 Halculate the 9 at t of the first deposit.+nter 8 3, &CYK 1%C1% 1, 1****, and M$ *.0olve for 9 /1,*6.

0tep % Halculate the 9 at t of the second deposit.+nter 8 %, &CYK 1%C1% 1, 1****, and M$ *.0olve for 9 /1%,354.

0tep Halculate the 9 at t of the third deposit.+nter 8 1%, &CYK 1%C1% 1, %****, and M$ *.0olve for 9 /%%,-4.

0tep $he sum of the future values gives you the answer, /5,-%.%5%( FV under dail! compounding Answer: a Diff: M

$he answer is a. 0olve for 9 as 8 1%, & C3- *.*11*, %,***, M$ *, and solve for 9 # /%,*%5.1.

*( PV under mont"l! compounding Answer: b Diff: M

0tart by calculating the effective rate on the second securityBCYK 1%8;M? 1*0olve for +99? 1*.41?.$hen, convert this effective rate to a semiannual rateB+99? 1*.41CYK %8;M? 1*.%1*4?.8ow, calculate the value of the first security as followsB8 1* × % %*, & 1*.%1*4C% -.1*-, M$ -**, 9 *, thus, /3,14-.6%.

1



( PV under non$annual compounding Answer: c Diff: M

9irst, find the effective annual rate for a nominal rate of 1%? with'uarterly compoundingB CYK , 8;M? 1%, and +99? # 1%.--?. &n orderto discount the cash flows properly, it is necessary to find the nominal ratewith semiannual compounding that corresponds to the effective rate calculatedabove. Honvert the effective rate to a semiannual nominal rate as CYK %,

+99? 1%.--, and 8;M? # 1%.16?. 9inally, find the as 8 % × 3,& 1%.16C% 3.*5, M$ -**, 9 *, and # /%,-1.4.

%( Value of missing pa!ments Answer: d Diff: M

9ind the 9 of the price and the first three cash flows at t .$o do this first find the present value of them.H9* -,-.64H91 1**H9% -**H9 4-*& 57 solve for 8 /,-.1-.

8 & 5 ,-.1-M$ *9 /-,433.53.

8ow solve for F.8 14& 5 -,433.539 *0olve for M$ /34-.

( Value of missing pa!ments Answer: c Diff: M

$here are several different ways of doing this. ;ne way isB9ind the future value of the first three years of the investment atYear .8 & 4. %,*4.6-M$ %,***9 /%,-6*.36.

9ind the value of the final /1*,*** at Year .8 4

& 4.M$ *9 1*,*** /3,1*3.3.

Add the two Year values (remember to "eep the signs right)./%,-6*.36 D /3,1*3.3 /14,4.*-.

8ow solve for the M$s over years through 5 (3 years) that have a of/14,4.*-.8 3



& 4. 14,4.*-9 *M$ /,4**.**.

( Value of missing pa!ments Answer: d Diff: M

$he proectGs cost should be the of the future cash flows. Ise the cash

flow "ey to find the of the first years of cash flows.

H9* *, H91 1**, H9% %**, H9 **, &CYK 1*, 8 /61.-5.

$he of the cash flows for Years %* must beB/,*** /61.-5 /%,-16.1.

$a"e this amount forward in time yearsB8 , &CYK 1*, %,-16.1, M$ *, solve for 9 /,-%.**.$his amount is also the present value of the 14year annuity.8 14, &CYK 1*, ,-%, 9 *, solve for M$ /14.64.

-( Amortization Answer: d Diff: M

8 %- × 1% & 6.-C1% 1%-,*** 9 *M$ /1,**3.-

o amorti<ationB+nterB 1 &8I$ 3* AM;K$&nterest /-1,4-.6-rincipal /5,*1-.5-2alance /11-,56.*-

$otal ayments - × 1% × /1,**3.- /3*,51.6*.

principalofKepayment?

/3*,51.6*

/5,*1-.5- *.15 1.5?.

3

( Amortization Answer: a Diff: M

=ivenB :oan alue /1**,***7 Kepayment eriod 1% months7Monthly ayment /5,-3.

8 1% 1**,***M$ 5,-39 *0olve for &CYK %.**? × 1% %.**?.

$o find the amount of principal paid in the third month (or period), use thecalculatorGs amorti<ation feature. +nterB &8I$ AM;K$ (to activate



the calculator@s amorti<ation feature).&nterest /1,356.6rincipal /4,4-4.132alance /44,161.63

4( Amortization Answer: c Diff: M

!e will use the amorti<ation feature of the >1*2.

+nter the loan detailsB8 * × 1% 3*& 5C1% *.4- 5*,***9 *M$ /4%.13.

$otal payments in the first % years are /4%.13 × % /14,45.6-.

8ow get the interestB1 &8I$ % AM;K$&nterest /13,*5%.ercentage of first two years that is interest isB/13,*5%.C/14,45.6- *.5%-5 5%.-5?.

6( %emaining balance on mortgage Answer: d Diff: M

0olve for the monthly payment as followsB8 1% × 1- 16*& 6.-C1% *.4*6 13*,***9 *M$ /1,-4-.-6.

Ise the calculatorGs amorti<ation feature to find the remaining principalbalanceB1 &8I$ 3 AM;K$&nterest / 6,3-6.rincipal / 16,*3%.-2alance /11,54.3

5

( %e&uired annuit! pa!ments Answer: d Diff: T

=oes on



&nfl. -? Ketires !elfare

* i 6? 1 % -

NOOOOOOOOOOOOOOOOOO

NOOOOOOOOOOOOOOO

NOOOOOOOOOOOOOOOOO

NOOOOOOOOOOOOOOOO

NOOOOOOOOOOOOOOO

N*,*** ,1** 3,*- 6,3%* QOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOQ

1%6,3-5 ROOOOOOOOOOOQ

1**,*** OOOOOOOOOOOOOOOOOOOOS (113,3*)

M$ M$ 1%,*15

0tep 1 $he retirement payments, which begin at t %, must beBt %B /*,***(1.*-)% /,1**.t B /,1**(1.*-) /3,*-.t B /3,*-(1.*-) /6,3%*.

0tep % 8ow we need enough at t % to ma"e the retirement payments ascalculated in 0tep 1. !e cannot use the annuity method, but we canenter, in the cash flow register, the followingBH9* ,1**.H91 3,*-.H9% 6,3%*.$hen enter & 6, and press 8 to find 8 /1%6,3-5.

0tep $he /1**,*** now on hand will compound at 6? for % yearsB/1**,***(1.*6)% /113,3*.

0tep $he net funds needed isB8eed at t % / 1%6,3-5!ill have ( 113,3*)8et needed / 1%,*15

0tep - 9ind the payments needed to accumulate /1%,*15. 0et thecalculator to T2eginT and then enterB8 %7 & 67 *7 9 1%,*15. 0olve for M$ /-,-*.

*

( %e&uired annuit! pa!ments Answer: a Diff: T

4- i6? 43 6 6- 63 64 66 65 5*

N

NOO . . . OON

OOOOOOOOONOOOOOOOOOO

NOOOOOOOOOO

NOOOOOOOOOOO

NOOOOOOOOOO

NOOOOOOOOOO

N

D1**,*** OOOOOOOOOOOOOOOOOOS D%1-,65%.-*

M$ M$ M$



(-*,***) (--,***) (3*,-**) (33,--*) (4,%*-) (%**,***) QOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOQ

(5-,-6.53) ROOOOOOOOOOOOOON

(145,3-3.3) Amount needed

alue of cash outflowsBAge 6- H9* (/ -*,***)

H91 ( --,***) (-*,***)1.1

H9% ( 3*,-**) (-*,***)(1.1)%

H9 ( 33,--*) (-*,***)(1.1)

H9 ( 4,%*-) (-*,***)(1.1)

H9- ( %**,***)0olve for 8 at 6? (/5-,-6.53).alue of /1**,*** at age 6-B /1**,***(1.*6)1* /%1-,65%.-*.0hortfall at age 6- /%1-,65%.-* /5-,-6.53 (/145,3-3.3).Halculate annual payments to e'ual this shortfallB8 1*7 &CYK 67 *7 9 145,3-3.3.0olve for M$ /1%,*1.-5.

1( %e&uired annuit! pa!ments Answer: c Diff: T

* i 6? 1 % , %, % *

P P P P P .. . . P P . . . P

(,3*.,5) %- %- %- ,* ,* AM$ AM$P P

%56.%- P

3%.1 ,3.6-

Halculate the 8 of payments in Years 1%BH9* *H91 %-H9% *& 60olve for 8 /%56.%-.ifference between the security@s price and of paymentsB/3*.5 /%56.%- /3%.1.Halculate the 9 of the difference between the purchase price and of

payments, Years 1%B8 %& 6 3%.1M$ *0olve for 9 /3.6-.Halculate the value of the annuity payments in Years %*B8 14& 6 3.6-9 *0olve for M$ /*.

%( %e&uired annuit! pa!ments Answer: a Diff: T

0tep 1 Halculate the cost of tuition in each yearBHollege Host $oday /1-,***, &nflation -?./1-,***(1.*-)3 /%*,1*1.(1) /%*,1*1../1-,***(1.*-)4 /%1,1*3.-1(1) /%1,1*3.-1./1-,***(1.*-)6 /%%,131.6(%) /,%.33./1-,***(1.*-)5 /%,%35.5%(%) /3,-5.6-./1-,***(1.*-)1* /%,.%(1) /%,.%./1-,***(1.*-)11 /%-,3--.*5(1) /%-,3--.*5.

0tep % 9ind the present value of college costs at t *B



H9* *H91- *H93 %*,1*1.H94 %1,1*3.-1H96 ,%.33H95 3,-5.6-H91* %,.%H911 %-,3--.*5& 1%7 solve for 8 /35,3-4.56.

0tep 9ind the of the /%-,*** gift received in Year B8 & 1%M$ *9 %-,***0olve for /14,45.-1.

0tep Halculate the of the net amount needed to fund college costsB/35,3-4.56 /14,45.-1 /-1,63.4.

0tep - Halculate the annual contributionsB2+=&8 Mode8 1%& 1%

-1,63.49 *0olve for M$ /4,4-.3*.

( %e&uired annuit! pa!ments Answer: b Diff: T

9ind the present value of the cost of college at t 1*. Ise the cash flowregister and remember that college costs increase each year by the rate ofinflation.t 1*B H9* /-,***.t 11B H91 /-,*** × 1.*4 /4,-*.**.t 1%B H9% /-,*** × (1.*4)% /*,*41.-*.t 1B H9 /-,*** × (1.*4) /%,643.-1.& 57 solve for 8 /13,15.41.

8ow figure out the amount of payments they should ma"eB8 1*& 5 %*,***9 13,15.41M$ /-,64.66 ≈ /-,66.

( FV of annuit! due Answer: a Diff: T

9irst, convert the 5 percent return with 'uarterly compounding to aneffective rate of 5.*6%?. !ith a financial calculator, 8;M? 5, CYK , +99? 5.*6%?. (onGt forget to change CYK bac" to CYK 1.)

$hen calculate the 9 of all but the final payment. 2+=&8 M;+ (1 CYK) 8 5, &CYK 5.*6%, *, M$ 1-**, and solve for 9 /%1,3%4.5. Youmust then add the /1,-** at t 5 to find the answer, /%,1%4.5.

-( FV of investment account Answer: b Diff: T

!e need to figure out how much money we would have saved if we didnGt pay forthe college costs.8 *& 1* *



M$ 1%,***0olve for 9 /-,11,11*.34.

8ow figure out how much we would use for college costs. 9irst get thecollege costs at one point in time, t %* using the cash flow register.H9* -6,*-H91 3%,1*6H9% 33,-3 × % 1%,51% (two "ids in school)H9 41,1*6 × % 1%,%13H9 43,*63H9- 61,11& 1*7 8 /,416.*%.

$his is the value of the college costs at year t %*. !hat we want is to"now how much this is at t *8 %*& 1* ,416.*%M$ *0olve for 9 /%,514,64.53.

$he amount in the nest egg at t * is the amount saved less the amountspent on college7/-,11,11*.34 /%,514,64.53 /%,5,%4%.41 ≈ /%,5,%4.

3( Effective annual rate Answer: c Diff: T

$ime :ineB

* 1% % %4 Months

* i ) #? 1 % %.%-

P P P P

6,*** 1*,***

8umerical solutionB0tep 1 'ind the effective annual rate (*) of interest on the ban+

deposit+AKaily (1 D *.*6*5C3-)3- 1 6.?.

0tep % 'ind the * of the investment

/6,*** /1*,***C(1 D i)%.%-

(1 D i)%.%- 1.%- 1 D i 1.%-(1C%.%-)

1 D i 1.1*%3 i *.1*%3 ≈ 1*.?

0tep ,ifference - .#/"% 0 1/"% - 2#%

9inancial calculator solutionB



Calculate *aily using interest rate conversion feature&nputsB CYK 3-7 8;M? 6.*57 ;utputB +99? +AK 6.?.Calculate * of the e3ual ris+ investment

&nputsB 8 %.%-7 6,***7 M$ *7 9 1*,***.;utputB & 1*.%-5 ≈ 1*.?.ifferenceB 1*.? 6.? %.*?.

4( on$annual compounding Answer: a Diff: T

$o compare these alternatives, find the present value of each strategy andselect the option with the highest present value.

;ption 1 can be valued as an annuity due. ;n your financial calculatorenterB2+=&8 mode (to indicate payments will be received at the start of the period)8 1%& 1%C1% 1M$ 1,***9 *0olve for /11,34.3.

;ption % can be valued as a lump sum payment to be received in the future. ;nyour financial calculator enterB+8 mode (to indicate the lump sum will be received at the end of the year)8 %& 1%C% 3M$ *9 1%,4-*0olve for /11,4.-.

;ption can be valued as a series of uneven cash flows. $he cash flows atthe end of each period are calculated as followsBH9* / *.**.H91 / 6**.**.H9% / 6**.** x (1.%*) / 53*.**.H9 / 53*.** x (1.%*) /1,1-%.**.H9 /1,1-%.** x (1.%*) /1,6%.*.H9- /1,6%.* x (1.%*) /1,3-6.66.H93 /1,3-6.66 x (1.%*) /1,55*.33.H94 /1,55*.33 x (1.%*) /%,66.45.



H96 /%,66.45 x (1.%*) /%,633.-.

$o find the present value of this cash flow stream using your financialcalculator enterB+8 mode (to indicate the cash flows will occur at the end of each period)* H97 6** H97 53* H97 1,1-% H97 1,6%.* H97 1,3-6.66 H97 1,55*.33 H97%,66.45 H97 %,633.- H9 (to enter the cash flows)7&CYK 1%C 7 solvefor 8 /11,%34.4.

Hhoose the alternative with the highest present value, and hence selectHhoice 1 (Answer a).

6( PMT and &uarterl! compounding Answer: b Diff: T

* i ) %?1 6* 61 6% 6 6 113 Utrs.

P P . . . P P P P P . . . P

D** D**M$ * * * M$ M$

9ind the 9 at t 6* of /** 'uarterly paymentsB8 6*7 & %7 *7 and M$ **.0olve for 9 /44,-*6.46.9ind the +AK of 6?, compounded 'uarterly, so you can determine the value ofeach of the receiptsB

+AK

*.*6 D1

1 6.%%?.

8ow, determine the value of each of the receipts, remembering that this is anannuity due. !ith a financial calculator input the followingB8 1*7 & 6.%%7 44,-*6.467 and 9 *.0olve for M$ /1*,466.46 ≈ /1*,465.

5( PV of an uneven 'F stream Answer: d Diff: T

arent@s savingsB >ealth Hare Hosts, Years 15%%B8 16 /1,***(1.1)15 /3,11-.51& 3 /1,***(1.1)%* /3,4%4.-*M$ 1** /1,***(1.1)%1 /4,**.%-9 * /1,***(1.1)%% /6,1*.%40olve for /1,*6%.43.* i ) 3?1 % 16 15 %* %1 %%

P P P . . . P P P P P

D1** D1** D1** 3,11-.51 3,4%4.-* 4,**.%- 6,1*.%4

/6,--.6 of >ealth care costs

1,*6%.43 of parents@ savings/4,4%.*6 :ump sum government must set aside

H9* *H9116 *H915 3,11-.51H9%* 3,4%4.-*H9%1 4,**.%-H9%% 6,1*.%4& 30olve for 8 6,--.6 of >ealth care costs.



Honse'uently, the government must set aside /6,--.6 /1,*6%.43 /4,4%.*6.Alternatively,H9* *H9116 1**H915 3,11-.51H9%* 3,4%4.-*H9%1 4,**.%-

H9%% 6,1*.%4& 30olve for 8 /4,4%.*6 :ump sum government must set aside now.

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