Annuity Formulas Research Articles

A Note on a (Not so) Well-Known Annuity Formula

A Note on a (Not so) Well-Known Annuity Formula

Conditional optimization of mortgage loan parameters

Subject. In the article, we calculate the period of a borrowing, in which the interest burden and monthly payments are minimal. Objectives. The aim is to create an algorithm to optimize the term of the mortgage loan, taking into account the amount of debt and interest rate of the loan. Methods. The study employs methods to analyze the formula of annuity payments of a mortgage loan, and to model the final optimization algorithm. Results. We developed an algorithm, to determine the optimal term of the loan, using the certain loan amount and interest rate. The study considers the case for banks, operating in Krasnoyarsk. Conclusions. The paper considers two parameters of a mortgage loan, i.e. the interest burden and the monthly payment, which is calculated, according to the annuity formula. Both parameters depend on the loan amount, the interest rate, and the period of the loan. However, the interest rate is set by the bank, so the only parameter that the borrower can change is the period of payment. By changing the term to maturity, it is possible to have a loan with minimum payments and interest burden. For the purpose of optimization, we consider both parameters simultaneously. Taking into account their versatile nature, we consider the optimal time, when payments and interest burden are minimized. The paper also reviews the case of optimization of credit parameters for construction enterprises of the Krasnoyarsk Krai, in various banks.

Comment

Comment

Building Modular Dividend Discount Models Using a 'Super Annuity Formula'

The dramatic increase in the importance of U.S. dividends since 2001 means that financial analysts may soon demand access to updated dividend discount models (DDMs). To address this need, we introduce a new “super annuity formula” that can be used in the modular construction of multiple-stage level-growth DDMs. We also use the super annuity formula to approximate a three-stage transitional-growth DDM very accurately. We show that these advanced DDMs are relatively robust to the input assumptions. Going forward, every financial analyst should have knowledge of and access to these updated DDMs, so as to capitalize on the growing importance of dividends.

Time Value Of Money And Its Applications In Corporate Finance: A Technical Note On Linking Relationships Between Formulas

Time Value of Money (TVM) is the most important chapter in the basic corporate finance course. It is imperative to understand TVM formulas because they imply important TVM concepts. Students who really understand TVM concepts and formulas can learn better in chapters of TVM applications. This technical note intends to present more complete TVM formulas and link their relationships from the growing annuity perspective to assist instructors in teaching and students in learning. Although TVM formulas are already available in the textbooks, this technical note provides another perspective of presenting and summarizing TVM formulas. The simplification or extension of the growing annuity formula to reach other TVM formulas is discussed in this note.

Assessing Economic Damages in Personal Injury and Wrongful Death Litigation: The State of Illinois

Forensic economics experts (FE) working with attorneys engaged in litigation, whether consulting, preparing a report, or testifying at deposition or trial, generally are expected to have some knowledge (1) of the state’s statutory and case law regarding allowable damages and methods; and (2) that certain topics (e.g., taxes, collateral sources) should not be mentioned or considered at certain times since a mistrial could result. This situation creates a tension: forensic economics experts are economics experts and are not attorneys, but nonetheless must have a reasonable understanding of the relevant state law. In this vein, the Journal of Forensic Economics (JFE) continues to publish a series of articles on the ways such damages are calculated in different state jurisdictions, one state at a time.2 The state of South Dakota is included in this issue and this paper adds Illinois to the list. Following the format of previous articles in this JFE series, Section II provides a listing of the controlling statutes, general case law, and court rules. Section III discusses the concept of earning capacity which appears throughout PI and WD case law in Illinois. Section IV discusses discounting to present value. Fringe benefits are discussed in Section V, while Section

Generalized Multiple Economy Cost-of-Living Ordinary Annuities From an Interest Theory Perspective

The comprehensive development and application of progressive levels of generalization of the concept of a classic ordinary annuity from an interest theory perspective with either discrete or continuous compounding (first level) is the focus of this article. The second level incorporates the effect of inflation, or cost-of-living, on the annuity rent specified by a second interest rate. Next, we allow the principal to fund multiple investment economies, each with its own cost-of-living interest rate (third level). The fourth level recognizes the need for different payment spans and nonuniform economy-dependent annuity rents and its utility is illustrated with a multinational corporation capital investment example. At the fifth level, cost-of-living interest rates are allowed to vary over time. A retirement example illustrates application of the most generalized annuity formula derived. Finally, useful tables presented throughout the article summarize a total of 29 annuity formulas.

Intra-Year Discounting Made Easy: A Comment

Abstract No abstract available.

Note on Deriving Annuity Formulas

Note on Deriving Annuity Formulas

A Consideration of Annuity Formulas

One of the mathematics courses taught at the freshman level in many colleges is Mathematics of Finance (or Mathematics of Investment). It is highly desirable for the student to have an understanding of the fundamental operations, procedures, and techniques in the course, but it should also be desirable for him to have a set of formulas, which if applied intelligently, would enable him to work problems rapidly. This is especially true in the treatment of annuities certain. It is toward a successful way to present these formulas that this note is directed.* The author has found the following table of formulas to be of very considerable help to the students in his classes. The formulas as presented in the following table have these advantages. (1) All formulas needed for the treatment of annuities certain in the ordinary freshman course are collected in one place. (The formulas as given here do not make allowances for perfectly general annuities, but these formulas do cover the three primary cases.) (2) In any one of the six classifications in which both sum and present value formulas are given in the table below, the formulas possess complete similarity. That is, the only difference between formulas is in the a} or sJ,i symbol. (3) In every instance the formulas are the basic formulas for Case I, ordinary annuities (defined later) with additional factors being included because of different data. The particular arrangement of factors is an aid to the student's memory. (4) In every instance the formulas use the same basic symbols with which the student is already familiar, with the exception of j, (which is defined below and to which the student may have been introduced in considering nominal rates of interest) and a; and sji which are defined early in the treatment of Case I annuities. This use of basic symbols eliminates the necessity for the student to memorize a new set of symbols for every new set of data, as is true in some treatments of the subject. (5) Transition from row to row or column to column of the table is quite simply performed, which is a definite aid to memory. (6) The formulas for deferred annuities are based on data which enables the student to treat every deferred annuity as an ordinary annuity. (7) To be sure, other forms of these formulas may lead to simpler computation in certain types of problems, but the formulas as given here lend themselves easily to solution for the periodic payment by a method involving multiplication instead of division. It seems that this more than compensates for the additional work necessitated in certain other types of problems.

Discussions: Simplification of an Annuity Formula

Discussions: Simplification of an Annuity Formula

Discussions: A Suggestion for Simplification of Annuity Formulas

Discussions: A Suggestion for Simplification of Annuity Formulas

Discussions: New Annuity Formulas for Payments made between Conversion Dates

Discussions: New Annuity Formulas for Payments made between Conversion Dates

Discussions: Derivation of Annuity Formulas without Series

Discussions: Derivation of Annuity Formulas without Series