Problem Set 6:
ACTSC 231 Mathematics of Finance, Fall 2010
Q1.
Carefully describe what each of the following symbols measures and calculate their
values to the nearest 0.0001:
(a) 200
a
(4)
10 6%
;
(b) 1200¨
s
(12)
20 4%
.
Q2.
Compare these four symbols ¨
a
n i
, ¨
a
(
m
)
n i
, a
(
m
)
n i
and a
n i
by calculating their values at
n
= 48,
m
= 12 and
i
= 5%.
Q3.
A loan of 20,000 is to be repaid in 20 years using the sinking fund method. You are
told that the sinking fund payment made at the end of each year is 744.31, and that
the annual effective interest rate
i
such that the amortization method based on
i
has
an annual payment equal to the total annual payment in the sinking fund method is
8.7%. Determine the annual effective interest rate
i
charged on the loan.
Q4.
For a loan of $1,000, level interest payments are made at the end of each year for 10
years with an annual effective interest rate of 5%, and the principal amount is repaid at
the end of 10 years. At the end of each year, the borrower makes level annual payment
to a sinking fund that earns interest at an annual effective rate of 4%. At the end of
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 Fall '09
 Chisholm
 Finance, Time Value Of Money, Annual Percentage Rate, Mortgage loan, Mathematical finance

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