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Lecture 8

Actuarial Science 2053 Lecture 8: Sep 28, 2015
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33 Pages
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Department
Actuarial Science
Course Code
Actuarial Science 2053
Professor
Steven Kopp

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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”
Definition – Interest Period
This is the time between two successive
interest calculations
for example, if interest is compounded
quarterly (i.e. interest is calculated and
paid 4 times a year), the interest period =
3 months
Your interest earns interest, as well as the principal!
Examples:!
Interest compounded semiannually => interest period is usually 6 months !1.
Interest compounded monthly => interest period is 1 month 2.
Interest can be earned more than once a year!
Example
Determine the interest earned on $10,000 over a
1-year period if interest is calculated at 6%,
compounded quarterly.
Solution
Notation/Definitions
P = original principal
= present value of S
= discounted value of S
S = accumulated value of P
n = term of investment in interest periods
m = number of interest periods per year
j
m
= nominal rate of interest,
compounded m-times a year
i = interest rate per interest period

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Description
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 Your interest earns interest, as well as the principal Definition Interest Period This is the time between two successive interest calculations for example, if interest is compounded quarterly (i.e. interest is calculated and paid 4 times a year), the interest period = 3 months Examples: Interest compounded semiannually => interest period is usually 6 months 1. Interest compounded monthly => interest period is 1 month 2. Interest can be earned more than once a year! Example Determine the interest earned on 10,000 over a 1year period if interest is calculated at 6, compounded quarterly. Solution NotationDefinitions P = original principal = present value of S = discounted value of S S = accumulated value of P n = term of investment in interest periods m = number of interest periods per year j = nominal rate of interest, m compounded mtimes a year i = interest rate per interest period
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