The mathematics of investment and credit is an important topic in actuarial science and financial mathematics. It covers key concepts like time value of money, interest rates, loans, bonds, project appraisal techniques, term structure of interest rates, etc. These form the foundation for more advanced topics in derivatives, asset pricing, risk management, etc.
In this article, we will summarize some of the key formulas and takeaways from the textbook ‘Mathematics of Investment and Credit’ which is used in actuarial exams like SOA Exam FM. This will help students prepare for actuarial exams and also apply these concepts in real world finance and investment situations.
Time Value of Money Formulas
The time value of money formulas allow us to value cash flows at different points in time and perform calculations like present value, future value, net present value etc.
Key formulas include:
Future Value = Present Value x (1 + Interest Rate)^Number of Periods
Present Value = Future Value / (1 + Interest Rate)^Number of Periods
For annuities or series of cash flows, we have:
Present Value of Annuity = Payment Amount x Annuity Factor
Future Value of Annuity = Payment Amount x Sinking Fund Factor
Where annuity factor and sinking fund factors depend on number of periods and interest rate. Tables are provided for these factors in exams.
Interest Rate Concepts
There are various interest rate concepts like nominal rates, real rates, effective annual rates etc. that are important.
Key takeaways include:
– Relationship between nominal, real, effective rates
– Force of interest notation and use in actuarial calculations
– Term structure of interest rates and Yield curve modeling
– Macaulay duration and modified duration for bond price sensitivity
Loans and Bonds
Loans and bonds are important fixed income securities.
Key concepts in this area include:
– Loan repayment schedules and calculations
– Types of loan repayment methods like equal installments, equal principal etc.
– Bond pricing formulas and calculations
– Yield rates for bonds
– Immunization and dedication strategies
The mathematics here involves time value of money formulas adapted suitably for loans and bonds.
Investment Appraisal Techniques
Investment projects need to be analyzed to determine if they are worth undertaking. Common appraisal techniques include:
– Net Present Value (NPV)
– Internal Rate of Return (IRR)
– Profitability Index (PI)
These methods use time value of money calculations to analyze investment cash flows and determine profitability.
The mathematics of investment and credit forms the backbone for all finance and investment calculations. Mastering the key formulas and concepts is critical for actuaries and financial analysts. This article summarized some of the main takeaways which students can use to reinforce their understanding.