Wisconsin Bookwatch (Oregon, WI USA)

Mortgages And Annuities
Yuri K. Shestopaloff
AKVY Press
142 Kennard Avenue, North York, ON, Canada, M3H 4M5
9780980966787, $57.95,

"Mortgages and Annuities: An Introduction" by mathematician Yuri K. Shestopaloff was specifically written and designed for undergraduate students, their teachers, and financial industry specialists needing a solid grounding in the mathematical foundations and computations associated with the development, implementation, and interpretation of financial investment instruments and their underlying formulas that are commonly associated with the purchase of buildings and investments for retirement. Informed and informative, "Mortgages and Annuities: An Introduction" is replete numerical examples, exercises, and illustrative problems making it especially appropriate as a curriculum textbook. Also very highly recommended for professional and academic library reference collections is Yuri K. Shestopaloff's "Mortgages And Annuities: Mathematical Foundations And Computational Algorithms" (9780980966770, $59.95).

From the Publisher

The book content is much based on the the previous study presented in the book "Science of Inexact Mathematics", which received good reviews (see reviews). So, the quality of content is commensurate. Besides, this book includes lots of problems and exercises and numerical examples.

Angel, review from (5 stars)

I read another book by this author, "Science of Inexact Mathematics", and wanted to get more details on debt instruments. It worked for me. Lots of examples, graphs, diagrams, problems and exercises make this book really a good teaching and professional text. (It would be nice to somehow get the answers to the problems.) I am not a novice in the business, but found a lot of new things and concepts which financial analysts have to know and understand. I would say that one will become fully comfortable with mortgages and annuities after working through this book. Another good thing is that the book starts from zero and almost effortlessly leads one to progress to an expert level; the entire transformation is done within two hundred pages. The book is easy to read and understand, and does not require the knowledge of sophisticated mathematics. In reviews of this book that I read, it was recommended for students. I also think that professionals should not overlook this book. It covers the fundamentals we need every day.

MortgageOrb (Interview with the author)


Yuri K. Shestopaloff Takes Mortgage Math To The Next Level

Phil Hall, Tuesday 08 June 2010 - 09:32:06


PERSON OF THE WEEK: In reviewing the roots of the economic crisis, it would not be flippant to question whether anyone involved in the mess - borrowers, lenders and regulators - had the ability to understand basic arithmetic. Going forward, the next generation of mortgage bankers may have to possess a better understanding of mathematical foundations and computations relating to loan products. This week, MortgageOrb speaks with Yuri K. Shestopaloff, author of the new book "Mortgages and Annuities: An Introduction" (published by AKVY Press), to discuss the role of computational algorithms and mathematical theories in reshaping the industry.

Q: What was the inspiration for your new book?

Shestopaloff: I first discovered problems with algorithms that are presently used in the financial industry when I was developing a financial software application. First, I used software engineering tools to improve system's performance. It helped, but I gradually realized that the mathematics are far from perfect. So, I started research, found a solution for that particular problem, published an article - then, the solution led to an attempt to tackle another problem, and so on.
You should understand the nature of this industry and its principal distinction from many other areas. In the aerospace industry, in which I continue to do some research, the result can be easily verified. You recognize or do not recognize some object, evaluate its parameters with required accuracy or not - you hit the target or miss it.
In the financial industry, however, such verification is very limited. For instance, there are many methods for computing the rate of return on an investment. The fund manager, in fact, can use any method, and nobody really knows which one is correct. Although there are some regulations, they are not very confining. All of these methods used to be considered to be independent.
In my earlier book, "Science of Inexact Mathematics," I proved that these methods are approximations of one parent method, called the internal rate of return (IRR), and showed what assumptions need to be made in order to obtain each approximate method. This way, the hierarchy of methods for computing rates of return was created, and their interrelations were discovered and mathematically defined. I showed limitations of the method that is supposed to be the industry standard for certain financial institutions and funds - called time-weighted rate of return - and I showed that this method generally produces the largest error.
In other words, I established the foundation on which objective valuation of rate of return and some other financial characteristics can be reliably built. Still, some principal ambiguities were present, but they were exposed, and some reasonable compromise solutions were found.

Q: But wouldn't it be fair to say that a good degree of ambiguity plays into the loan origination process? How can you answer that with mathematical equations?

Shestopaloff: Mortgage-related mathematics has slacks and ambiguities that can be used by either side - lender or borrower - although the lender is usually more knowledgeable. The difference in total payment amount can be several percent and, in some instances, more. I really would like people to know these details when they think about borrowing or lending money, as well as to understand all implications and mechanisms of quick debt accumulation, when they deal with compounding, which is usually the case in the lending business.
Another thing I wanted to show is that mortgages and annuities can be arranged in a very flexible way to tailor the needs of the borrower and the lender to a particular situation. It was shown that a mortgage equation can be directly derived from the same IRR equation. Therefore, it can be used as the basis for any fancy mortgage, as well as for any mortgage reconfiguration and restructuring when there is a need.
This approach delivers a very powerful instrument, but this is a double-edged sword. Rightly used, it could easily help the majority of people to avoid foreclosures, but it can also provoke bankruptcy, depending on the original purpose.

Q: Your book is different from other books about mortgages and annuities because it covers computational algorithms. Why is it important for mortgage bankers to have a strong knowledge of computational algorithms?

Shestopaloff: In my experience, mortgages and other investment vehicles are processed by software applications. When I consult system designers and programmers developing these applications, one of my duties is to tell them what mathematical and computational algorithms to use. I am trying to follow industry conventions, but the choice is not always unique - far from that. When I am trying to discuss the problem with clients, I often discover that they have a vague idea, if any, of what I am trying to convey, until I explain all the nuances.
For instance, one can compute the interest rate for shorter periods using the compounding or non-compounding approach, continuous or discrete, and so on. If mortgage brokers and software developers understood what kind of enormous flexibility they could have if they used the IRR equation as the basis for their computations, then many foreclosures could be avoided.
One more reason: The interest rate cannot be computed directly, the appropriate equation is solved numerically. Having efficient computational algorithms makes routine computations and analytical studies go a lot faster. In general, equations of this type have multiple solutions. Finding the right one requires knowledge of algorithms.

Q: Many people have blamed the push for loan quantity over loan quality as driving the crash of the U.S. mortgage banking industry. Is it possible that an absence of mathematical analysis contributed to the crisis that faced the U.S. mortgage banking industry during the past two

Shestopaloff: Any real phenomenon is defined by many factors. The mortgage market is only one factor in the whole picture. One should also look at the source of money and its stability. In that case, much instability and the resulting problems came from uncontrolled and unfounded monetary emissions.
The next "money producing well" was collateralized debt obligations and all the associated manipulations, such as repackaging, off-balance-sheet assets, involvement of international funds, etc. - all of these things worked as a powerful money printing machine. In such a situation, it is difficult to understand how much money is actually in the economy.
In fact, money is nothing - it is a phantom. People forget that money is the measure of wealth, but not the wealth itself. Any misbalance between the measure and the real thing causes problems sooner or later.
However, mathematical analysis could at least expose all consequences of lending a certain amount of money to population with known assets and incomes. Such analysis could also predict the price increase in the housing market, region by region, based on historical data and simulation models, when you know how much money was lent to home buyers and how many building permits were issued. Based on this data, it is possible to evaluate the dynamics of creditworthiness of a population.
If such an analysis were to be done and be widely exposed to the public, it could somehow influence the mortgages' quality. In the borrowing spree, it would probably not influence it much. However, the data was there, and we could have made the right inferences.

this content item is from Mortgage Orb


Interactive Computer Corporation (

Newsletter, June, 2010



Interactive Computer Corporation gained recognition in part for its great customer service and the “can do” philosophy of its founder, Midwest banker Michael “Mike” Straziuso. The other part was being able to compute some of the most complex mortgage loan programs, limited only by the imagination of the mortgage marketing gurus at some of the most well-known and respected lenders. Many lenders used ICC as their test lab, both for document development and for providing a test platform for mortgage computations. For those seeking a background in the subject of mortgage mathematics, we rarely recommend anything other than a “how to” calculator course to allow even relatively unsophisticated loan officers, brokers and lenders to compute their own APRs and cash flows.

Today, we are privileged to recommend a more theoretical book, “Mortgages and Annuities: An Introduction” by a renowned mathematician, Yuri Shestopaloff. But before we proceed further with the review of this fine book, we must warn you that the material is presented at the college-level and the book reads like a textbook on specialized mortgage mathematics. There are mathematical formulas which require some knowledge of calculus at the college level. This book is not for everyone, but should be required reading for mortgage and data processing professionals who want to know more about the computations behind mortgages and annuities. The author is quick to point out that mortgages are “just another subset of financial instruments whose quantitative description is based on the IRR (Internal Rate of Return) equation. Understanding the IRR and the various methodology of its computation is the key to understanding this book and its approach to mortgages and annuities. The author notes that there are ambiguities in the methodology to calculate the Internal Rate of Return which may concede an advantage to either the borrower or the lender, depending on which methods are used in the calculations. Knowing which algorithms to use in calculating APRs and projected cash flows is as important as knowing the creditworthiness of the borrower. "Mortgages and Annuities: An Introduction” contains a number of numerical examples, exercises, and illustrative problems which should serve the professional well in aiding in their understanding of the subject material. And other than the mathematical underpinning of the text, the author takes you from a zero understanding of the subject material to an expert level almost effortlessly. This is not a reference book per se, but a “core foundation” book that should be in every professional’s library. And, unfortunately, like most college textbooks, the answers to the work problems at the end of the chapter are not provided. However, it is well worth your time and effort to master its subject matter.

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