This Mini Case Study can be found in your textbook in Chapter $4($p$.192).$ Please review the case and then answer questions a$-$g using the attached excel spreadsheet.$$

Assume that you are nearing graduation and have applied for a job with a local bank. The bank$$s evaluation process requires you to take an examination that covers several financial analysis techniques. The first section of the test addresses discounted cash flow analysis. See how you would do by answering the questions listed below.$$

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$$of an initial $$100$ after $3$ years if it is invested in an account paying $10\%$ annual interest?

$(2)$What$$s the$$present value$$of $$100$ to be received in $3$ years if the appropriate interest rate is $10\%?$

c$.$ We sometimes need to find out how long it will take a sum of money $($or something else, such as earnings, population, or prices$)$ to grow to some specified amount. For example, if a company$$s sales are growing at a rate of $20\%$ per year, how long will it take sales to double?

d$.$ If you want an investment to double in $3$ years, what interest rate must it earn?

e$.$ What$$s the difference between an ordinary annuity and an annuity due? What type of annuity is shown below? How would you change the time line to show the other type of annuity?

f$.(1)$What$$s the future value of a $3-$year ordinary annuity of $$100$ if the appropriate interest rate is $10\%?$

$(2)$What$$s the present value of the annuity?

$(3)$What would the future and present values be if the annuity were an annuity due?

g$.$ What is the present value of the following uneven cash flow stream? The appropriate interest rate is $10\%,$ compounded annually.