MA170 Week 5: Compound Interest  Part II
Name: ____SOLUTIONS____________
Lab:
Fall 2010
1.
[6
marks
]
Consider an investment opportunity offering an interest rate of
j
1
= 5%
:
(a) How much must be invested on November 1, 2010 to accumulate to $10 000 by August 1, 2012 at the
given rate of interest?
There is one full year and 273 days between Nov.1 2010 and Aug. 1 2012:
OR: 1 year 9 months
t
= 1 +
273
365
=
638
365
t
= 1 +
9
12
=
21
12
P
= 10000
e
°
638
=
365(0
:
05)
:
= $9163
:
13
P
= 10000
e
°
21
=
12(0
:
05)
:
= $9162
:
19
(b) If $1000 is invested at this rate of interest, what will the investment be worth in 6 months time?
S
= 1000
e
0
:
05(6
=
12)
:
= $1025
:
32
(c) Assuming that in°ation will be 2% over the next year, what is the real rate of interest?
e
0
:
05
= 1 +
j
)
j
=
e
0
:
05
°
1
:
= 0
:
051271096
i
real
=
0
:
051271096
°
0
:
02
1 + 0
:
02
= 0
:
03065793725 = 3
:
07%
2.
[15
marks
]
Canada Premium Savings Bonds are 10 year investment instruments issued by the government of
Canada. They can be purchased in denominations of $100, $300, $500, $1000, $5000 and $10 000 and are
cashable on each anniversary and 30 days thereafter.The interest rates are usually set in advance for the ±rst three
years, and increase each year. After three years, they °uctuate with market conditions.
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 Fall '11
 F.Vinette
 Math, Interest Rates, Interest

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