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UNIT 11  :  MATHEMATICS OF INVESTMENT

LESSON 3: PRESENT VALUE HOMEWORK QUESTIONS

Quick Review:

Present Value:

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 ½ 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 ½ 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.