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 UNIT 11  :  MATHEMATICS OF INVESTMENT

 LESSON 3: PRESENT VALUE

 

Example 1:

a)  Puneet wishes to have $20 000 available in 4 years in order to purchase a new car.  If  interest is 5%/a compounded quarterly, how much should she invest today in order to amount to $20 000 in 4 years?.

 Solution:

In this example, we are given the final or future amount and we wish to find the amount to invest today in order to accumulate to that $20 000 in 4 years.  The amount we are trying to find here is called the Present Value of $20 000 due in 4 years at 5%/a, compounded quarterly.

 

The appropriate time line is shown below.  Since there are 16 interest periods, we will put a mark every 3 months over the 4-year period.

 

                       0       1       2       3                                                                                                     14   15  16

                       

20000(1.0125)-16                                                                                                                                              20000

 

 

 

 

The formula for the  Present Value of some future amount can be determined by re-arranging our formula for compound interest and solving for P.

                       

 

Text Box: Formulas:
 	
Text Box: PV = present value of a future amount                           
n = number of interest periods
i  = interest rate per interest period as  
      as a decimal
A = accumulated or future amount
 

 

 

 

 


                                                                                                                       

 

 

 

 

Example 2:

Mr. And Mrs. Trinh would like to have $500 000 available when they retire in 20 years.  How much should they invest now if interest is 6%/a, compounded semi-annually?

Solution:

 

The appropriate time line is shown below.  Since there are 40 interest periods, we will put a mark every 6 months over the 20-year period.

 

                       0       1       2       3       4                       .     .    .                                                        38   39  40

                       

500000(1.03)-40                                                                                                                                                                                                      500000

 

They should invest $153 278.42 today to achieve their goal.

 

Example 3:

John would like to have $10 000 available to start up his own DOT COM business in 3  years.  How much should he invest now if interest is 7.44%/a, compounded monthly?

Solution:

He should invest $8005.06 today to achieve his goal.

 

 

 

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