R Programming for Actuarial Science

3 Financial Mathematics (1): Interest Rates and Valuing Cashflows

Peter McQuire

3.1 Introduction

One of the most fundamental tasks of the actuary is to estimate, using particular assumptions, how much money is required at a point in time such that we can expect to be able to make contractual payments in the future. To estimate this amount we will generally need to make three assumptions – the level of interest rates (or investment returns) expected in the future, the probability that the payment or payments will be made, and an assumption regarding the amount of the payment. In this chapter we simplify the situation and concern ourselves only with future payments which are certain and for a known amount; only an interest rate assumption is required. We will introduce the other factors in later chapters.

The principal objective of this chapter is therefore to develop methods to calculate the amount required in respect of a series of future cashflows, based on a particular set of interest rates. These interest rates may reflect the expected future investment return on the assets we hold; often, however, they may be adjusted to allow for a degree of prudence, other commercial factors, or simply be prescribed by legislation.

There are various types of interest rates used in practice, such as the force of interest, effective interest rates, and nominal interest rates. The majority of this chapter will discuss the force of interest; however we will also compare the concepts of effective ...