1
1
Lecture 3:
Topic: Mathematics of Finance
Reading
H&P, Ch 5.
Reading for this lecture
H&P, Ch 5, Sect 5.1  5.2;
(also refer back to Ch 4, pp. 167168)
Homework for Tutorial in Week 2
Ex 5.1, pp. 200201, problems 1, 3, 9, 11.
Ex 5.2, pp. 204205, problems 3, 11, 15, 19.
2
Compound Interest
Suppose $100 is invested at 8 percent per
annum. Interest is earned and reinvested
at the end of every quarter.
What is the compound amount after 1 year?
Principal
= $100
Nominal
interest rate = 8%
per year
Quarterly interest rate = 8/4 =
2% per quarter
Number of
quarters
=
4
3
Compound Interest
End of Qtr 1: S = 100(1 + 0.02)
= 102
End of Qtr 2: S = 102(1 + 0.02)
= 104.04
= 100(1 + 0.02)(1 + 0.02) = 100(1 + 0.02)
2
= 104.04
End of Qtr 3: S = 104.04(1 + 0.02)
= 106.12
= 100(1 + 0.02)
2
(1 + 0.02) = 100(1 + 0.02)
3
= 106.12
End of Qtr 4: S = 106.12(1 + 0.02)
= 108.24
= 100(1 + 0.02)
3
(1 + 0.02) = 100(1 + 0.02)
4
= 108.24
4
Compound Interest Formula
S = P(1 + r)
n
(
formulae for ‘cheat sheet’)
where
P
is the original principal
n
is the number of
conversion periods
r
is the rate of interest
per conversion period
S
is the compound amount after n periods
S – P is amount the compound interest earned
5
Find S
, given P, r and n
Suppose $1,000 is invested at 5%.
What is the
compound amount after 4 years if
interest is
accumulated (a) annually, (b) semiannually?
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 Spring '10
 drea
 final payment, conversion periods

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