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?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '10
 drea
 final payment, conversion periods

Click to edit the document details