Time value of money analysis 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 $50, $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 10 percent, annual compounding?
(2) What’s the present value of $100 to be received in 3 years if the interest rate is 10 percent, annual compounding?
c. What annual interest rate would cause $100 to grow to $125.97 in 3 years?
d. If a company’s sales are growing at a rate of 20 percent 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?
f. (1) What is the future value of a 3-year, $100 ordinary annuity if the annual interest rate is 10 percent?
(2) What is its present value?
(3) What would the future and present values be if it were an annuity due?
g. A 5-year $100 ordinary annuity has an annual interest rate of 10 percent.
(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 $3 a day for her retirement. Every day she places $3 in a drawer. At
the end of each year, she invests the accumulated savings ($1,095) in a brokerage account with an
expected annual return of 12 percent.
(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 10 percent.
j. (1) Will the future value be larger or smaller if we compound an initial amount more often than annually,
for example, semiannually, holding the stated (nominal) rate constant? Why?
(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 10 percent compounded semiannually? Compounded quarterly? Compounded daily?
(4) What is the future value of $100 after 3 years under 10 percent semiannual compounding? Quarterly
compounding?
k. When will the EAR equal the nominal (quoted) rate?
