The Difference Between Nominal and Effective Interest Tables And Nominal and Effective Rates of Return (includes associated discussion and reply)
Authors: Essley P.L. 
Published: December 2007

Several different types of interest tables are commonly used by petroleumengineers. Conventional (or year-end) and midyear tables are based on aneffective interest rate i, while continuous interest tables are expressed as afunction of a nominal rate j. To avoid confusion, a rate of return i calculatedusing midyear or year-end tables should be called an effective rate of return, while a rate of return j calculated using continuous interest tables should becalled a nominal rate of return. When either type of rate is known, the othercan he determined readily from a simple equation. Conversion factory to adjustreceiving income other than at the end of a period are derived and their usediscussed.

Introduction

The use of interest tables seems to be quite simple. However, there are anumber of different types of commonly used interest tables that give differentresults. For instance, for a single problem one engineer using conventionalinterest tables might calculate a rate of return of 41 per cent. another usingmidyear tables might calculate a rate of return of 55 per cent, while stillanother using continuous interest tables might calculate a rate of return of 44per cent. This occasionally can result in considerable confusion when twonegotiating companies use different types of interest tables, or when differentdepartments of a company use different types of tables. The purpose of thispaper is to point out the relationship between the various types of interesttables, to show how results compare, and to show how answers obtained using onetype of table can be converted to equivalent answers from other types oftables.

Nomenclature and Symbols

In addition to the different types of tables in common use, there are anumber of ways to express compound interest to account for different patternsof income or to simplify the solution of different types of interest problems. A set of interest tables. of any type, may include a compound interest table. apresent worth table, several annuity tables, a sinking fund table, a partialpayment table, an equivalent nominal rate table. auxiliary tables, or othertables. Such interest tables are related through simple mathematicalexpressions. Unfortunately, there is no uniformity in what we call thesefactors, or tables. Identical tables, obtained from different sources, may havecompletely different, apparently unrelated, names (i.e., present value vsprincipal, which will amount to a given sum). On the other hand, similarnomenclature is often used with the different types of tables. Thus, a set ofconventional interest tables and set of continuously compounded interest tablesmight both include a table labeled "present worth", which will containdifferent factors within the tables. A similar lack of standardization existswith regard to the mathematical symbols used in interest equations. Such lackof standardization might cause a casual user of interest tables to becomeconfused. The nomenclature and symbols used in this paper are similar to thoseused by the Financial Publishing Co.

Conventional Compound-Interest Equations and Tables

Conventional interest tables are based on the premise that interest iscompounded periodically and that income, or payments, is received at the end ofeach period. The following are the common ways that compound interest can beexpressed.

Amount of $1 at Compound Interest

The amount of compound interest is often called the amount of 1", the"single payment compound amount". or the "amount". It shows how $1 at compoundinterest will grow. Expressed as an equation, it is

(Amount of 1) = s = (1 + i) . . . (1)

where i = the uniform rate of interest, fraction n = the number of periodsof interest conversions, and I indicates conventional interest equations, whereincome is received and compounded at the end of each period. The amount at theend of each period is obtained by multiplying the amount at the beginning ofthe period by the ratio of increase (1 + i). A compound interest table can beconstructed for any rate by successive multiplication by the ratio ofincrease.

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