IME VALUE OF MONEY ANALYSIS $($LO#$1)$

You have applied for a job with a local bank. As part of its evaluation process, you must take an examination

on time value of money analysis covering the following

questions:

a$.$ Draw time lines for $(1)$ a $$100$ lump sum cash flow at the end of Year $2$; $(2)$ an ordinary annuity of $$100$

per year for $3$ years; and $(3)$ an uneven cash flow stream of $$250,$ $$100,$ $$75,$ and $$50$ at the end of Years $0$

through $3.$

b$.1.$ What$$s the future value of $$100$ after $3$ years if it earns $4\%,$ annual compounding?

$2.$ What$$s the present value of $$100$ to be received in $3$ years if the interest rate is $4\%,$ annual

compounding?

c$.$ What annual interest rate would cause $$100$ to grow to $$119\mathrm{.}10$ in $3$ years?

d$.$ If a company$$s sales are growing at a rate of $10\%$ annually, how long will it take sales to double?

e$.$ What$$s the difference between an ordinary annuity and an annuity due? What type of annuity is shown

here? How would you change it to the other type of annuity?

$0123$

$0$ $$100$ $$100$ $$100$

f$.1.$ What is the future value of a $3-$year, $$100$ ordinary annuity if the annual interest rate is $4\%?$

$2.$ What is its present value?

$3.$ What would the future and present values be if it was an annuity due?

g$.$ A $5-$year, $$100$ ordinary annuity has an annual interest rate of $4\%.$

$1.$ What is its present value?

$2.$ What would the present value be if it was a $10-$year annuity?

$3.$ What would the present value be if it was a $25-$year annuity?

$4.$ What would the present value be if this was a perpetuity?

h$.$ A $20-$year$-$old student wants to save $$5$ a day for her retirement. Every day she places $$5$ in a drawer. At

the end of each year, she invests the accumulated savings $($$$1,825)$ in a brokerage account with an expected

annual return of $8\%.$

$1.$ If she keeps saving in this manner, how much will she have accumulated at age $65?$

$2.$ If a $40-$year$-$old investor began saving in this manner, how much would he have at age $65?$

$3.$ How much would the $40-$year$-$old investor have to save each year to accumulate the same amount

at $65$ as the $20-$year$-$old investor?

i$.$ What is the present value of the following uneven cash flow stream? The annual interest rate is $4\%.$

$01234$ Years

$0$ $$100$ $$300$ $$300-$$$50$

j$.1.$ Will the future value be larger or smaller if we compound an initial amount more often than

annually $($e$.$g$.,$ semiannually, holding the stated $($nominal$)$ rate constant$)?$ Why?

$2$

$2.$ Define $($a$)$ the stated $($or quoted or nominal$)$ rate, $($b$)$ the periodic rate, and $($c$)$ the effective annual

rate $($EAR or EFF$\%).$

$3.$ What is the EAR corresponding to a nominal rate of $4\%$ compounded semiannually?

Compounded quarterly? Compounded daily?

$4.$ What is the future value of $$100$ after $3$ years under $4\%$ semiannual compounding? Quarterly

compounding?

k$.$ When will the EAR equal the nominal $($quoted$)$ rate?

l$.1.$ What is the value at the end of Year $3$ of the following cash flow stream if interest is $4\%$

compounded semiannually? $($Hint: You can use the EAR and treat the cash flows as an ordinary

annuity or use the periodic rate and compound the cash flows individually.$)$

$0246$ Periods

$0$ $$100$ $$100$ $$100$

$2.$ What is the PV$?$

$3.$ What would be wrong with your answer to parts $(1)$ and $(2)$ if you used the nominal rate, $4\%,$

rather than the EAR or the periodic rate, I$\_$Nom$/2=4\%/2=2\%,$ to solve the problems?

m$.1.$ Construct an amortization schedule for a $$1,000,4\%$ annual interest loan with three equal

installments.

$2.$ What is the annual interest expense for the borrower and the annual interest income for the lender

during Year $2?$coomcbankings