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 $$\frac{1}{1+rt}=1-dt⟺(1-dt)(1+rt)=1,$$

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

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 $$\begin{array}{r}365=31\text{(Jan)}+28\text{(Feb)}+31\text{(Mar)}+30\text{(Apr)}+31\text{(May)}+30\text{(Jun)}+\\ 31\text{(Jul)}+31\text{(Aug)}+30\text{(Sep)}+31\text{(Oct)}+30\text{(Nov)}+31\text{(Dec)},\end{array}$$ except in leap years, where there are 29 days in February (and 366 days in the year).