Week 1 Detailed Learning Outcomes

At the end of your learning for this week, you should be able to master the following contents.

Actuarial Practice #

Definition of an “actuary” #

Provide an initial description of what an actuary is, and main areas of practice.

Actuarial Techniques #

Pooling and insurance #

Describe and explain why and how the pooling of risks is beneficial, and how this underpins the business of insurance.

Accumulation under simple interest rate \(r\) #

Master the formula $$A = P(1+rt),$$ where \(A\) is the accumulated amount of \(P\) with simple interest \(r\) per period.

Discount under simple discount rate \(d\): #

Master the formula $$P = A(1 - dt),$$

where \(P\) is called the discounted amount of \(A\) with simple discount \(d\) per period.

The relationship between (simple) \(r\) and \(d\) #

We have $$\frac{1}{1+rt} = 1- dt \Longleftrightarrow (1-dt)(1+rt) = 1, $$

which also means $$t = 1,\quad r = \frac{d}{1-d},\quad d = \frac{r}{1+r}.$$

In commerical bills: #

Understand some basic vocabulary such as in this context:

• \(A\) = Face Value
• \(P\) = Purchasing Price

A year has 365 days #

Calculate the exact number of days between two dates. The number of days in a normal year is \begin{align*} 365 = 31\text{(Jan)} + 28\text{(Feb)} + 31\text{(Mar)} + 30\text{(Apr)} + 31\text{(May)} + 30\text{(Jun)} + \\ 31\text{(Jul)} + 31\text{(Aug)} + 30\text{(Sep)} + 31\text{(Oct)} + 30\text{(Nov)} + 31\text{(Dec)}, \end{align*} except in leap years, where there are 29 days in February (and 366 days in the year).