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Present Value

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 UNIT 11 : MATHEMATICS OF INVESTMENT

 LESSON 3: PRESENT VALUE HOMEWORK QUESTIONS

 

Quick Review:

Present Value:

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
 

 

 

 

 


 

 

 

Homework Questions: (see solutions below)

1. Calculate the present value for each future amount below. Show a time line diagram for c & d.

a) $3000 due in 8 years at 4%/a, compounded semi-annually.

b) $10 000 due 9 years at 6.35%/a, compounded annually.

c) $25 000 due in 5 years at 4.54%/a, compounded quarterly.

d) $50 000 due in 4 years at 4.25%/a, compounded monthly.

e) $40 000 due in 6 years at 5.5%/a, compounded semi-annually.

 

2. On the birth of their grandson, Carole and John wish to invest for his education. If the investment pays 8%/a, compounded monthly, how much should they invest today in order to provide $20 000 when he turns 18?

 

3. Barry wishes to have $3000 when he turns 19 to buy his own stereo system. He is now exactly 15 years old. How much should he invest today if interest is 6%/a, compounded quarterly?

4. Ramona wishes to have $20 000 available in 6 years in order to buy furniture for an apartment. How much should she invest today if interest is 6.5%/a, compounded annually for the first two years and 5.4%/a, compounded monthly for the last 4 years?

 

5. Fatima owes her parents $8000 which she is scheduled to repay in 5 years time. She received a bonus from her work and wishes to repay the loan now. How much should she pay if interest is 4.8%/a, compounded quarterly?

 

 

Solutions:

1. Calculate the amount for each loan.

a) $3000 due in 8 years at 4%/a, compounded semi-annually.

b) $10 000 due 9 years at 6.35%/a, compounded annually.

c) $25 000 due in 5 years at 4.54%/a, compounded quarterly.

d) $50 000 due in 4 years at 4.25%/a, compounded monthly.

e) $40 000 due in 6 years at 5.5%/a, compounded semi-annually.

 

Solutions:

 

 

 
.

 

 

 

 

0 1 2 3 18 19 20

25000(1.01135)-20 25000

 

 

 

 

 

 

 

0 1 2 3 46 47 48

50000(1.00354)-48 50000

 

 

 

 

 

 

2. On the birth of their grandson, Carole and John wish to invest for his education. If the investment pays 8%/a, compounded monthly, how much should they invest today in order to provide $20 000 when he turns 18?

Solution:

Hence John and Carole should invest $4761.25 today.

 

 
Solution:

 

Hence Barry should invest $2364.09 today.

 

 

4. Ramona wishes to have $20 000 available in 6 years in order to buy furniture for an apartment. How much should she invest today if interest is 6.5%/a, compounded annually for the first two years and 5.4%/a, compounded monthly for the last 4 years?

Solution:

The time line below shows the value of the $20 000 as it is brought back in time, first 4 years, then 2 more years

 

Now

0 1 2 3 4 5 6

20000(1.0045)-48 $20 000

$16 122.52

$16122.52(1.065)-2

=$14214.57

 

 

Hence Ramona should invest $14 214.57 today.

 

5. Fatima owes her parents $8000 which she is scheduled to repay in 5 years time. She received a bonus from her work and wishes to repay the loan now. How much should she pay if interest is 4.8%/a, compounded quarterly?

 

Solution:

 
 


Hence Fatima could repay the loan by paying $6302.02 today.

 

 

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