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UNIT
9 :
MATHEMATICS OF INVESTMENT
LESSON 2:
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.