# Tag Archives: Math

## Fast Formulas #6: Finding the Time

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 | | 2 Comments

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

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

Posted in Fast Formulas, Math | | 5 Comments

## Fast Formulas #3: Pool Average Life with CPR Prepayments

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

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

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)

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

Posted in Fast Formulas, Math | | 9 Comments

## Puzzle #4: Bond Pricing

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

Posted in Bonds, Fun, Math, Puzzles | | 12 Comments

## Puzzle #3: A Better Answer

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

Posted in Fun, Math, Puzzles | | 5 Comments