Simple Interest and Simple Discount
S = P (1+ rt )
P = S (1+ rt )1
1
S = P (1 dt )
P = S (1 dt )
I = Prt = S P
D = Sdt = S P
Compound Interest
S = P (1+ i )n
i = jm/m
P = S(1+ i ) n
j
jm and jp are equivalent if (1 + j m ) m = (1 + p ) p
m
p
Equivalent Ra
Actuarial Science 2053 2016-2017 Midterm Exam Information
1. The Midterm Exam is scheduled for Tuesday, December 13, 2016. The exam is a 3-hour
exam from 9:00 am to noon.
2. The exam will be written in the following rooms:
Last Name
A to J
K to Z
Building
Module 1 Part 1
Economic Security and Insecurity
What is Economic Security?
It is part of a persons total welfare
It is a state of mind or a sense of well being by which a person is relatively certain
that he/she can satisfy basic needs and wants, both pr
Module 1 Part 1
Economic Security and Insecurity
What is Economic Security?
It is part of a persons total welfare
It is a state of mind or a sense of well being by which a person is relatively certain
that he/she can satisfy basic needs and wants, both pr
Module 1
The Nature of Economic Insecurity
Economic insecurity is the opposite of economic security
a person is unable to achieve a sense of well being due to a fear that
present and future needs will not be satisfied
Economic insecurity consists of one o
Comparison of Social and Private Insurance
Question: Is Social Insurance really insurance?
To answer this question, we need to understand the similarities between Private and
Social Insurance
To do that, we need to know some of the characteristics of priv
Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are two
parties:
The lender and the borrower
If you deposit money into a bank account,
you are lending money to the bank
Consider the following transa
Chapter 2 Compound Interest
Fundamental Compound Interest Formula
(section 2.1)
Compound Interest
The interest earned in any given period of
time is added to the principal and it
thereafter earns interest
the interest is said to be compounded
and your in
Determining the Term of an Annuity
(section 3.5)
Given: S or A, R, i
Determine: n
Method
You can use logs to solve:
S=R
s n |i
or
A=R
an |i
Problem
n will rarely be an integer
will need to calculate a final payment that
is different from R in order to h
Determining the Rate and Time (2.5)
(I)
Determining the Rate
Given: P, S, n
Determine: i
Start with: S = P(1 + i )n
(1+ i )n = S/P
(1+ i ) = (S/P)1/n
i = (S/P)1/n 1
most of the time, you are asked to solve for
jm = mi
Example 2.5.1
At what nominal rate j2
Compound Interest at Changing Interest
Rates (section 2.7)
In all examples/exercises so far, the interest
rate was assumed to be constant throughout
the term of the investment
frequently, however, the interest rate
changes over the term of a loan or
inve
Annuities Where Payments Vary
(section 4.4)
Not all annuities have a level series of
payments; instead we are going to look at
annuities where the payments change every
period
Two Standard Types
(I)
Payments vary in terms of a constant
ratio
these are an
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
Chapter 4 General and Other Annuities
General Annuities (section 4.1)
General annuities are annuities (either
ordinary or due) where the interest period
and the payment period are NOT the same
1.Semi-annual payments, quarterly interest
2.Monthly payments,
Discounted Value of An Ordinary Simple
Annuity (section 3.3)
Consider the following
An ordinary simple annuity consisting of
n-payments of $1
we wish to determine the present value, A,
of these payments at the beginning of the
term
that is, what is the
Chapter 3 Simple Annuities
Introduction
Suppose you deposit $500 every 6-months
for 2-years.
How much will you have accumulated
immediately after the 4th deposit if j2 = 6%?
0
500
1
500
2
500
3
500
4
S
i = 0.06/2 = 0.03
S = 500 + 500(1.03) + 500(1.03)2 +
Perpetuities (section 4.3)
A perpetuity is an annuity where the
payments begin on a fixed date and
continue forever
since payments continue forever, it is
meaningless to calculate accumulated
values
we will only look at the present value
of perpetuities