Chapter 9
Review problems
9.1
Interest rate measurement
Example 9.1. Fund A accumulates at a simple interest rate of 10%. Fund B accumulates at
a simple discount rate of 5%.
Find the point in time at which the forces of interest on the two funds are equal

Continuous Annuities (section 4.4)
A continuous annuity is an annuity where
the payments are made continuously
throughout the year
It would be a special case of an annuity
that is payable more frequently than
interest is compounded, where m
It is more

There are many different functional forms of
the accumulation function, a(t)
However, there are two functions that are
used most often in the financial world
These two functions represent two different
types of interest calculation:
1. Simple Interest (se

Chapter 2 - Equivalence Equations
Equations of Value (section 2.1)
Concept of Dated Values
All financial decisions must take into
account the time value of money
For example,
Example 2.1.1
A man originally owes $2000 at the end of 4
years. Instead, it is

Other Simple Annuities (section 3.4)
(I) Annuity Due
An annuity-due is an annuity where the
periodic payments are due at the beginning
of each payment interval
term of an annuity-due starts at the time of
the 1st payment and ends one period after
the dat

Example 1.7.4
You can borrow money from three different
lenders who offer the following rates:
Bank A: i(2) = 8.1%
Bank B: i(12) = 7.95%
Bank C: i(4) = 8.04%
Rank the banks from best rate (to borrow) to
worst.
Solution to 1.7.4
Accumulating/Discounting wi

Steps of Performing Arbitrage
Using long/short positions of the securities, set
Arguments
up two portfolios having identical cash flows.
Let V1 and V2 be the values of these two
portfolios, respectively.
We want to show that V1 = V2, otherwise there
is a

Interest Rate Conventions
Zero-Coupon Bonds
Bond Basics-Notation
Examples
One year zero-coupon bond:
P(0,1)=0.943396
Pay $0.943396 today to receive $1 at t=1
Yield to maturity (YTM) = 1/0.943396 - 1
= 0.06 = 6% = r (0,1)
Two year zero-coupon bond:
P(0,2)=

AS 2553a Mathematics of nance
Formula sheet
November 29, 2010
This document contains some of the most frequently used formulae that are discussed in the course.
As a general rule, students are responsible for all denitions and results appearing in proposi