You just passed your CFP exam and are a certified financial planner. You meet with many clients and want to display your knowledge.

Prepare a video presentation of no more than $5$ minutes using the questions in this case to explain the Time Value of Money to new clients. All new clients will review the video before your first meeting so the meeting can be productive with knowledgeable clients. The last question in the case is particularly important.a$.$ Draw time Ines for $(1)$ a $$100$ lump sum casn IIow at the ena or Year an oranary annuly or

$$100$ per year for $3$ years, and $(3)$ an uneven cash flow stream of $-$$$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.