MATH 420

Math 420: Actuarial Mathematics

Prerequisites: STAT 301

Credit Hours: (4)

This course is designed to assist students in preparing for two actuarial exams—the Financial Mathematics (FM) Exam and the Probability (P) Exam—conducted by the Society of Actuaries (SOA) and the Casualty Actuarial Science (CAS). The semester is divided into approximately two equal halves. The first portion is for Exam FM, while the second is for Exam P. All topics included in the SOA and CAS syllabi for these exams will be covered. 

 

Content

Topics covered for Exam FM:  

1. Time Value of Money
   
   1. simple and compound interest
   2. nominal and effective interest
   3. continuous compounding,
   4. constant and variable interest rates
   5. present and future value of continuous stream of payments
2. Annuities
   
   1. constant, arithmetic, and geometric cash flows
   2. finite and infinite terms of annuities
   3. present and future value of ordinary annuities
   4. present and future value of annuity dues
   5. continuous annuities and perpetuities,
3. Bonds
   
   1. pay/face value, coupon rate, effective yield, yield rate
   2. types of bonds: zero-coupon, premium/discount, and callable

Topics covered for Exam P: 

1.  Combinatorics and Probability 
   1. counting techniques, permutations and combinations
   2. sample space, events, and probability rules
   3. probability of events, including Bayes’ theorem and law of total probability
2. Common Probability Distributions
   
   1. discrete distribution
   2. continuous distribution
3. Mathematical Expectation and Summary Measure
   1. expected value
   2. variance, moments
   3. median, mode and percentiles
   4. Sums of Independent Random Variables
   5. poisson distribution 
   6. Normal distribution
4. Multivariate Probability Distributions
   
   1. joint, marginal, and conditional distributions
   2. expected value, variance, covariance/correlation of multiple variables
5. Order Statistics and Linear Combinations
   
   1. Distribution of order statistics 
   2. linear combinations of independent random variables

 

Detailed Description of Conduct of Course

Course delivery methods will include classroom lectures, structured discussions, group work, and applied examples.

 

Student Learning Outcomes

Students will learn the fundamental principles of financial mathematics and probability theory, and develop the ability to apply these principles to actuarial problem solving. Throughout the course, they will strengthen their analytical and problem-solving skills while establishing a foundational understanding that supports professional growth, further study, and career opportunities in insurance, pensions, and finance.

By the end of the course, students will:

1. develop an understanding of the core concepts and techniques that are central to the Exam P and Exam FM provided by SOA/CAS.
2. acquire insight into actuarial mathematics, the pathways to an actuarial career, and the core mathematical tools for further study.

 

Assessment Measures

Students’ performance will be assessed through tests, homework assignments, and other possible measures, with the number and weights determined at the instructor’s discretion.

 

Other Course Information

None

 

Review and Approval

January 6, 2026