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Answer & Explanation:Unit 4 Discussion Write a 1 page paper, double spaced that summarizes the Seminar and what you learned.  Seminar Attached.unit_4.pptx
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Unit 4
Chapter 3- Time Value of Money
Importance of TVM
TVM is not only used in corporate finance, but also in
personal finance
o Calculating car payments
o Mortgage payments
o Retirement planning
Simple Interest
Compute simple interest earned on 1 year $100
deposit that earns 7% per year and compute the
future value (FV).
Solution
Interest=Principal x Interest Rate
Interest = $100 x 0.07= $7
Future Value is the sum of the original deposit plus
interest earned:
$100 + $7= $107
Simple vs Compound
Simple interest is interest earned on original principal
Compound interest is interest earned on interest
Example using timeline for a 2 year investment of $100
at 7% interest.
0____________1___________________2
$100
$100*7%=
$107*7%=
$107
$114.49
Future Value of a Sum
• The book will show the algebraic formula for FV.
• Will we practice using Excel:
Your grandmother gives you $1,000 upon graduation.
You decide to invest it for 40 years. Your interest is 10%
per year. What is the future value of your investment?
Excel
• Formulas tab
• Insert Function – far left hand side (fx)
• Change drop box to “all” and type in future value
in the box. Click “go”
• Make sure FV is highlighted and click “ok”
• Rate= .10
• Nper= 40
• PMT= 0
• PV= -$1000
• FV= $42,259.26
Cont.
We can calculate the interest earned by subtracting
the original principal:
Interest Earned = FV-PV
$45,259.26-$1,000= $44,259.26
What would be the interest earned if the example
were simple interest (instead of compound)?
Solution
$1,000 x 0.10= $100
$100 x 40 = $4,000 (total interest earned)
Difference
$44,259.56 – $4,000 = $40,259.26
Now that you see the difference, do you think it is
important to start saving for retirement early?
FV Example
Joe expects to receive a gift of $1,000 when he
graduates one year from today. Joe can invest his gift
at 6% compounded annually and he would like to use
the funds in four years to purchase an engagement
ring for Mabel. How much will he have in four years to
spend on a ring?
Find the FV
Solution
I would do it this way:
Find FV
Rate : .06
Nper: 4
Pmt: 0
PV: -1000
FV: $1,262.48
The book uses it this way:
2 step
First you discount the $1,000 to the
PV of today
Solve for PV
Rate: .06
Nper: 1
Pmt: 0
FV: 1000
PV = $943.40
Second, find the FV in 4 years
Rate: .06
Nper: 4
Pmt: 0
PV: -943.40
FV= $1,191.02
Compounding Period
If you are measuring the future values in months (as
your Nper), you would need to adjust the interest rate.
If the interest rate is stated as annual, you divide by 12
for your Rate input.
FV Example
If $100 is placed in an account that earns a nominal
4%, compounded quarterly, what will it be worth in 5
years?
Solution
Solve for FV
Rate: .04/4
Nper: 20
Pmt: 0
PV: -100
FV = 122.02
Future Value of Mixed
Streams
Using Excel:
You expect to receive $100 at the end of the first
period, $200 at the end of the second period, and
$300 at the end of the third period. You will earn 10%
for 6 periods.
Payment
Years until Year 6
FV
$100
5
$161.05
$200
4
$292.82
$300
3
$399.30
Total
$853.17
Solve for Rate
20 years ago you invested $5,000. The account is now
worth $19,348.42. What was your annual interest rate
(or rate of return)?
Excel:
Formulas
Insert Function
Rate
Nper= 20; Pmt= 0; PV= 5000; FV=19348.42 solve: Rate= 7%
Multiple Compounding
Periods per Year
FV of $1,500 deposit after 20 years with an annual
interest rate of 8% compounded quarterly:
Excel
Formulas
Insert Function
FV
Rate= .02(.08/4); Nper= 80 (20×4); Pmt= 0; PV= 1500
Solve FV= 7313.16
Present Value
• You buy a bond that will be worth $42,259.26 in 40
years. Your interest rate is 10%. How much should
you pay for the bond today?
• Rate= .10
• Nper= 40
• PMT= 0
• FV= -$42,259.26
Solve for PV= $933.72
PV Example
In 6 years you are going to need $1,000. How much
will you need to invest today at 7% in order to save
the money you need?
Solution
Solve for PV
Rate: .07
Nper: 6
Pmt: 0
FV: 100
PV = 666.34
PV Example
What is the present value of $2,000 to be received in
six years if interest rates are 8% compounded
semiannually? (round to the nearest whole dollar)
Solution
Solve for PV
Rate: .08/2
Nper: 12
Pmt: 0
FV: 2000
PV = 1,249
…
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