Tag Archives: Math

Fast Formulas #6: Finding the Time

Posted on June 30, 2015 by Win Smith

  The Fast Formulas on this blog provide shortcut calculations for financial instruments such as mortgages and bonds. Most formulas involve the symbol n to represent the number of periods (e.g. years or months) until the end of the instrument. Usually … Continue reading →

Posted in Bonds, Fast Formulas, Math | Tagged , , , , | 2 Comments

Fast Formulas #4: Geometric Series (One of the Tricks)

Posted on October 18, 2012 by Win Smith

In Fast Formulas #3: Pool Average Life with CPR Prepayments, I presented Formula 3.1, a shortcut calculation for the average life of a loan pool under a constant prepayment assumption.  I mentioned that Formula 3.1 was derived by using “a … Continue reading →

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Fast Formulas #3: Pool Average Life with CPR Prepayments

Posted on July 22, 2011 by Win Smith

Fast Formulas #2: Average Life of Mortgage (Amortizing with Balloon) presented a compact formula for calculating the average life of a mortgage that pays as scheduled until it is paid off with a “balloon” payment before the scheduled end of its term.  It occurred to … Continue reading →

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Fast Formulas #2: Average Life of Mortgage (Amortizing with Balloon)

Posted on July 17, 2011 by Win Smith

Fast Formulas #1: Average Life of Mortgage (as Scheduled) showed a quick way to calculate the weighted average life (“WAL”) of a fixed-rate mortgage that pays as originally scheduled.  I found this formula (which is probably not original) by substituting the standard  level … Continue reading →

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Fast Formulas #1: Average Life of Mortgage (as Scheduled)

Posted on July 14, 2011 by Win Smith

The weighted average life (“WAL”) of a mortgage is the average time until principal is repaid.  It is also the average amount of time that the principal is outstanding.  Recall that for a standard fixed-rate mortgage with level payments, the principal … Continue reading →

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Puzzle #4: Bond Pricing

Posted on July 7, 2011 by Win Smith

Here’s another puzzle I’ve used to teach bond math. It’s not hard, but it requires some understanding of bond concepts that I will explain as we go (I beg the patience of bond mavens). Suppose you are the financial advisor … Continue reading →

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Puzzle #3: A Better Answer

Posted on June 2, 2011 by Win Smith

Puzzle #3 asked for the weighted average life (“WAL”) of the principal payments for a 30-year mortgage that is cut short by a balloon payment at 15 years. The following information was provided: $100,000 Principal; 5% Interest Rate; $536.82 Level … Continue reading →

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Derivative of the Quotient

Posted on April 25, 2011 by Win Smith

Given a function F = G/H, the first derivative is usually expressed as (HG’ – H’G)/(H^2) But this is equivalent to: (G’ – F H’)/H The second form seems to be easier to implement in some cases and requires less … Continue reading →

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Last Week’s Bond Refunding Optimization Talk

Posted on April 25, 2011 by Win Smith

I enjoyed giving a talk last week at the UC Denver Operations Research Seminar.  There were many excellent questions from those attending, who included representatives from investment banking and the public sector.  Many thanks to Alex Engau for the opportunity … Continue reading →

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Puzzle #3: Mortgage with Balloon

Posted on April 15, 2011 by Win Smith

Puzzle #1 posed the question: given a $100,000 mortgage at 5% with monthly payments of $536.82 for 30 years, what is the average life of the principal payments? The puzzle was to be solved with just a few simple calculations. … Continue reading →

Posted in Fun, Math, Puzzles | Tagged , , , , , , , | 22 Comments