Siming Zhu
AEM 4260_Fixed Income
September 16, 2008
Homework 2
Ch 2 – Q 2 & 9; Ch 3 – Q 12
Q2.
Suppose that a life insurance company has guaranteed a payment of $14 million to a
pension fund 4.5 years from now.
If the life insurance company receives a premium of
$10.4 million from the pension fund and can invest the entire premium for 4.5 years at an
annual interest rate of 6.25%, will it have sufficient funds from this investment to meet
the $14 million obligation?
Using an
annual interest rate of 6.25%
, the $10.4 million invested by the life insurance
company for 4.5 years will grow to be:
FV
t=4.5
= $10.4 million(1+.0625)
4.5
FV
t=4.5
= $10.4 million(1.31365)
FV
t=4.5
= $13.662 million.
Using an annual interest rate of 6.25%, the $10.4 million will grow to approximately
$13.662 million in 4.5 years, which is not enough to meet the $14 million obligation.
Using a
semiannual interest rate of 3.125%
(6.25/2), the 10.4 million invested by the
life insurance company for nine 6months periods will grow to be:
FV
t=9
= $10.4 million (1+.03125)
9
FV
t=9
= $10.4 million (1.31909)
FV
t=9
= $13.719 million
$10.4 million compounding semiannually at 3.125% will grow to approximately
$13.719 million in nine 6months periods (4.5 years), which is still not enough to meet
the $14 million obligation.
Q9.
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 Fall '06
 BOGAN,V.
 required yield, total future dollars

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