How to Use the Solutions Manual for Broverman Without Losing Your Mind
The textbook Mathematics of Investment and Credit by Samuel Broverman is the standard reference for actuarial students preparing for Exam FM. The solutions manual that accompanies it exists to walk through the exercises in each chapter. It is not optional if you are working through the book seriously. I went through Broverman cover to cover while studying for Exam FM. The solutions manual is essentially a step-by-step answer key for the exercises in the book. Each problem gets its full derivation, not just the final number. That matters because many of these questions have multiple paths to the answer and the manual shows the intended one. The manual typically covers five major areas: basic time value of money, annuities and cash flow streams, bonds and bond valuation, loan amortization schedules, and then the longer chapters on duration, convexity, and immunization. You will see the same notation everywhere. v for discount factor, i for effective interest, s-double-dot and a-double-dot for annuity-due. The book establishes this early and the manual never explains it again. If you are confused about the double-dot notation, go back to Chapter 1. The manual assumes you already know it.
Here is a practical issue I ran into repeatedly. The manual sometimes skips steps in the annuity chapters, especially around geometric progression annuities where payments grow at a rate other than the interest rate. I spent an entire evening trying to reverse-engineer one solution involving an increasing annuity where the growth rate differed from the discount rate. The trick I ended up using was to separate the problem into two components: treat it as a standard annuity first, then apply the growth adjustment factor separately. Once I did that, the manual's shortcut made sense. It is not a gap in the manual. It is just a compression of steps that assumes you have seen the decomposition before. Another thing people miss: the manual uses both the recursive method and the formula method interchangeably. In the bond chapter, some solutions set up the price as a sum of discounted cash flows while others use the premium-discount formula directly. The exam does not care which you use as long as the answer is correct. But on practice problems, mixing methods carelessly causes sign errors. I started writing out which method I was using at the top of each solution. It saved me from losing points on three separate practice problems. If you are looking for the manual itself, search for Mathematics Of Investment And Credit Solutions Manual along with the edition you are using. The fourth edition and fifth edition have different problem sets. Make sure you are not pulling solutions from the wrong edition. I learned that the hard way when I grabbed a PDF that turned out to be for the third edition. Half the answers did not match my exercises because Broverman revised several chapters between editions.
The manual is reliable for the standard problems. It is less helpful when you encounter the more unusual variations in the later chapters. The immunization section, for example, has problems that require constructing a portfolio that satisfies multiple constraints simultaneously. The manual gives one valid answer but does not always explore why alternative portfolios work or fail. In those cases, I found it useful to cross-reference with practice exams from the Society of Actuaries rather than relying solely on the manual. One limitation you should be aware of: the manual does not cover every edge case in the textbook. Some of the more challenging problems in the cash flow matching and liability management sections leave you to figure out parts of the reasoning on your own. If you hit a wall there, the SOA sample questions and the practice exams from the actuarial website tend to fill in the gaps better than the manual does. My recommended workflow is straightforward. Read the chapter first. Attempt the problems without looking at anything. Then go through the manual problem by problem, comparing your approach to theirs. Write down where you diverged. Those divergence points are where you actually learn. Skipping ahead to the answers before doing the work defeats the purpose entirely and wastes the time you would spend figuring it out yourself.
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The manual works best when you treat it as a tutor rather than an answer sheet. Use it to check your logic, not to bypass the struggle of getting there. The problems in Broverman are designed to build the kind of fluency you need for the exam. The manual just helps you verify you are on the right track.
