FIN 200:
Personal Finance
Topic 7-Project and Annuities
Lawrence Schrenk, Instructor
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Project Guidelines
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Downloading and Opening the
Project Spreadsheet
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Login to Blackboard
‘Course Documents”
Right click on project link, and “Save target
as...”
Close Blackboard
Double-click on project to open Excel
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Do you have Excel installed?
Use only this version of the project.
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Blackboard
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Opening the Project
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“Disable Macros?”–Yes
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What are ‘macros’?
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Inside the Project
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Click on the ‘index’ tab.
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Project Index Page
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Project Worksheets
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Excel ‘Lingo’ and Basic Procedures
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Worksheets (or ‘Sheet’)
Cells
References, “G20”
Protected versus Unprotected Cells
Click on Cell, Type, Hit Return
Two Worksheet ‘Inputs’
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Text
Numbers
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Text Inputs
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Numbers Inputs–Auto-Functions
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Dollar Values
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Percentage
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Input 12% as ’12’ like Calculator
Calculations
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2000 to $2,000–No commas in numerical inputs.
Calculations are Programmed and Automatic
No text in numbers cells!
#VALUE!
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Numbers Inputs–Auto-Functions
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Project Guidelines
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Instructions on Individual Worksheet
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See Project Web Page
Perspective:
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2-3 Years after Final Year of Education
Realistic Data
Web Research
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Common Sites
Unique Sites
Ask for Help
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Progress
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One or Multiple Worksheets per Topic
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Periodic Review
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Worksheets Organized by Topic, not Chapter.
Weekly Progress Expectations
Blackboard–’Project 1 Review’, etc.
Not Graded
Final Submission
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Don’t put anything in the ‘Digital Drop Box’.
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CAUTION
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Do not give out private information to web
sites.
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Best Case–Insurance agents will call you for
years.
Worst Case–Identity Theft.
Project web page has suggestions for
individual worksheets.
I can always help.
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Uploading the Project I
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Uploading the Project II
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Requirements I
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Own a car (financed with a car loan),
Own a house (financed with a mortgage),
Have a credit card on which you have some
(non-trivial) balance.
Have the following insurance policies:
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Medical
Life
Auto, and
House.
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Requirements II
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Save for retirement.
Plan to leave a bequest (i.e., money in you
will) to someone or an organization, e.g., a
charity.
If you want to alter these, let me know, but
you need to do something in each category.
Complete all worksheets.
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Annuities: Present and
Future Value
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Annuities
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An annuity is
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NOTES:
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A series of constant payments
That occur at regular intervals and
Do not continue forever.
The first payment occurs next period (not now).
Payments are annual. We will do non-annual later.
If the payments go on forever, it is called a
‘perpetuity’ (but we don’t need to study them).
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Annuity Example
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You want to buy a car by saving $2,000 per
year, rather than depositing the entire amount
(present value) now.
This is the more common way to save for a
large purchase or for retirement.
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Not many of have the present value of our
retirement needs right now!
To have $1,000,000 at your retirement in 50 years
(at 3% interest), deposit $228,107.08 today. ▪
Why the low interest rate? ▪
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Annuity Time Line
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The constant cash flows of a 3 year annuity
of $100.00 per year at 10%:
I/Y
0
I/Y
1
2
3
PMT
PMT
PMT
10%
0
I/Y
10%
1
$100.00
10%
2
$100.00
3
Payments begin
next period.
$100.00 ▪
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Uses of the Annuity Calculation
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Our Key Calculation
Present Value of an Annuity
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‘Borrowing’ Problems (Loans)
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How much can I borrow (PV)?
How much are my payments (PMT)?
What interest rate am I getting (I/Y)?
How long will it take (N)? ▪
Future Value of an Annuity
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‘Savings’ Problems (Retirement Fund)
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How much will I have (FV)?
Ditto ▪
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Present and Future Value of an
Annuity
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We can either find the present value or the
future value of an annuity
I/Y
I/Y
0
1
2
3
PV
PMT
PMT
PMT
I/Y
0
I/Y
I/Y
1
PMT
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I/Y
2
PMT
Note the asymmetry! ▪
3
PMT
FV ▪
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The Annuity Calculation
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For an annuity we have five possible inputs:
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But we will often only use four of them at a time:
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PV, FV, I/Y, N, PMT
PV, I/Y, N, PMT
FV, I/Y, N, PMT
As before, you input three variable and your
financial calculator will give the fourth as a
result.
Make sure the unused input, PV or FV, is zero.
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Future Value with a Calculator
How much do we have after 3 years if we
save $200 per year beginning next year and
the interest rate is 12%?
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1.
2.
3.
4.
Input 3, Press N
Input 12, Press I/Y
Input 200, press +/-, press PMT (you get -200)
Press CPT, FV to get 674.88, i.e., $674.88
NOTE: As before one (and only one) of the dollar
value inputs must be negative.
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Future Value with a Calculator
12%
0
1
$200.00
12%
12%
2
$200.00
3
$200.00
$674.88
3
12
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-200
674.88
Remember to press CPT, before FV (if necessary).
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Future Value of an Annuity Practice
Problems
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How much will you have if you save $100.00
per year for 25 years at 8%?
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How much will you have if you save $1000.00
per year for 5 years at 7%?
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$7,310.59
$5,750.74
How much will you have if you save $1.00
per year for 50 years at 10%? ▪
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$1,163.91 ▪
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Present Value with a Calculator
What is the present value of $200 per year
for 3 years beginning next year, if the
interest rate is 12%?
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1.
2.
3.
4.
Input 3, Press N
Input 12, Press I/Y
Input 200, press +/-, press PMT (you get -200)
Press CPT, PV to get 480.37, i.e., $ 480.37
NOTE: As before one (and only one) of the dollar
value inputs must be negative.
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Present Value with a Calculator
0
$480.37
3
12%
12%
1
$200.00
12
480.37
2
$200.00
-200
12%
3
$200.00
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Remember to press CPT, before FV (if necessary).
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Present Value of an Annuity Practice
Problems
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What is the present value of $100.00 per year
for 25 years at 8%?
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What is the present value of $1000.00 per
year for 5 years at 7%?
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$1,067.48
$4,100.20
What is the present value of $1.00 per year
for 50 years at 10%? ▪
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$9.91 ▪
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Using PV and FV Keys
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There are situations in which you need all five
buttons, i.e., both PV and FV.
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Savings Problems/Future Value Problems
You have already accumulated some savings.
You want to know how much you will have in the
future (FV) taking into account you currently have
some amount saved (PV).
Your accumulated savings is PV.
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PV and FV Timeline
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How much do we have after 3 years if we
save $200 per year beginning next year, the
interest rate is 12%, and we already have
$500?
12%
12%
0
1
$500.00
$200.00
12%
2
$200.00
3
$200.00
???
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PV and FV problems
How much do we have after 3 years if we
save $200 per year beginning next year, the
interest rate is 12% and we have already
saved $500?
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Input 3, Press N
Input 12, Press I/Y
Input 500, press +/-, Press PV (you get -500)
Input 200, press +/-, press PMT (you get -200)
Press CPT, FV to get 1377.34, i.e., $ 1377.34
NOTE: In this type of problem both dollar inputs
must be negative.
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PV and FV with a Calculator
0
$200.00
12%
1
12%
$200.00
2
12%
$200.00
3
$200.00
$ 1377.34
3
12
-500
-200
1377.34
Remember to press CPT, before FV (if necessary).
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PV and FV Practice Problems
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How much do we have after 3 years if we
save $500 per year beginning next year, the
interest rate is 12% and we have already
saved $1,000?
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$3,092.13
How much do we have after 3 years if we
save $200 per year beginning next year, the
interest rate is 8% and we have already
saved $500? ▪
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$1,279.14 ▪
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