Calculation with interest rate (Lecture summary)

EAR (Equivalent Annual Rate).

used to illustrate the full percentage cost of overdrafts and any type of account
that can be in credit and also go overdrawn.

takes account of the basic rate of interest
Types of interest (Lecture Summary)
The mathematics that underlies costing loans and pensions and predicting movements
in the financial market all relies on what is called the time value of money.
Money in the hand now is worth more than money in the futu
QUICK SUMMARY OF 2M
PART 1: MODELLING
1. Maths behind the modelling
1.1. Linear functions. A straight line has equation
y = kx + p,
where k is the gradient and p is an intersection with yaxis. If we are
given two distinct points (x1 , y1 ), (x2 , y2 ) on
Department of Mathematics
Financial Modelling 1: Models from Economics
Natural logarithms (i.e. logarithms to the base e) are denoted log in this course; these logarithms
are often denoted ln, especially on calculators.
The arguments of trigonometric func
Financial Modelling
Sheet 2: Compound interest, annuities, mortgages and
securities
Compound interest
1. Calculate the accumulated value of 1000 invested for 5 years in an account bearing (i) simple
interest, (ii) compound interest at a rate of 6% per ann
APR and AER (Lecture summary)
Doubling Time.

A savings account pays interest at an annual rate of i%. Show that capital
invested in this account doubles over approximately (0:35+0:70=i) years. Let the
doubling time be TD then P(TD) = 2P0. Thus 2P0 = P0(
QUICK SUMMARY OF 2M
11
2.9. Market surveys. Information about the demand for a particular
product can be estimated by using market surveys: Would you pay
p1 , p2 , p3 , . . . pN 1 , pN for BrandX? Assume that
p1 < p2 < < pN 1 < pN .
Presumably everybody w
8
PART 1: MODELLING
2.4. Market equilibrium (Market price). The market balances
where q s (p) = q d (p). If q s is strictly increasing and q d is strictly decreasing as a function of price, then there is a unique value of the price
pe is such that the num
Thursday, 17th December, 2009
@ University
w of Glasgow
EXAMINATION FOR THE DEGREES OF
MA. AND B.Sc.
13.00 pm. to 14.30 pm.
Mathematics 2M  Financial Modelling
An electronic calculator may be used provided that it does not have
a facility for either text
Friday, 6th August, 2010 2.30 pm. to 4.00 pm.
5 Universit
QfGlasgowy
Emmi
EXAMINATION FOR THE DEGREES OF
M.A. AND B.Sc.
Mathematics 2M Financial Modelling
An electronic calculator may be used provided that it does not have
a facility for either textual
QUICK SUMMARY OF 2M
5
2. Models from Economics and Finance
2.1. Simple Interest.
Simple interest is paid only on the original balance.
P is the principal the original (at time t = 0) deposit.
r is the annual rate of interest.
I is the total interest pai
MATH3075/3975
FINANCIAL MATHEMATICS
ChristianOliver Ewald and Marek Rutkowski
School of Mathematics and Statistics
University of Sydney
Semester 2, 2014
Students enrolled in MATH3075 are expected to understand and learn all
the material, except for the