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School

Western University
Department

Actuarial Science

Course Code

Actuarial Science 2053

Professor

Steven Kopp

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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