Time Value of Money - Future Value and Present Value

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Time Value of Money
Annuities
Perpetuities
Kinds of Interest Rates
Future Value of an Uneven Cash flow
Probability Distribution
Standard Deviation
CAPM
Security Market Line
Bond Valuation
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The Balance Sheet
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The Time Value of Money

Present Value	How much you got now.
Future Value	How much what you got now grows to when compounded at a given rate

I give you 100 dollars. You take it to the bank. They will give you 10% interest per year for 2 year.

The Present Value = $ 100
Future Value = $121.

FV= PV (1 + i )^N

FV = Future Value
PV = Present Value
i = the interest rate per period
n= the number of compounding periods

Determine Future Value Compounded Annually
What is the future value of $34 in 5 years if the interest rate is 5%? (i=.05)

FV= PV ( 1 + i ) ^N
FV= $ 34 ( 1+ .05 ) ⁵
FV= $ 34 (1.2762815)
FV= $43.39.

Determine Future Value Compounded Monthly
What is the future value of $34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166)

FV= PV ( 1 + i ) ^N
FV= $ 34 ( 1+ .004166 ) ⁶⁰
FV= $ 34 (1.283307)
FV= $43.63.

Determine Present Value Compounded Annually
You can go backwards too. I will give you $1000 in 5 years. How much money should you give me now to make it fair to me. You think a good interest rate would be 6% ( You just made that number up). (i=.06)

FV= PV ( 1 + i ) ^N
$1000 = PV ( 1 + .06) ⁵
$1000 = PV (1.338)
$1000 / 1.338 = PV
$ 747.38 = PV

O.K. so you give me $ 747.38 today and in 5 years I'll give you $1000. Sound fair?? You will get 6% interest on your money.

Determine Present Value Compounded Monthly
Here's that last one again, but with monthly compounding instead of annual compouding. (i equals .06 divided by 12, because there are 12 months per year so 0.06/12=.005 so i=.005)

FV= PV ( 1 + i ) ^N
$1000 = PV ( 1 + .005) ⁶⁰
$1000 = PV (1.348)
$1000 / 1.348= PV
$741.37 = PV