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Category Archives: Fast Formulas
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
Tagged Bond Math, Fast Formulas, Math, Mortgage Math, Time Value of Money
2 Comments
Happy 0 0 1 0 0 1 0 0 0 0 1!
Most systems for representing numbers are a combination of the visible and invisible. In the familiar baseten system, we represent numbers by linking visible digits to an invisible scaffold of powers of ten. For example, 534.08 implies the respective multiplication … Continue reading
Posted in Fast Formulas, Math, Music
Tagged Fundamental Theorem of Arithmetic, Prime Numbers, Pure Math, Representing Numbers, WellTempered
3 Comments
Fast Formulas #1 (Followup): New Insight into an Old Formula
Ugarte (Peter Lorre): You despise me, don’t you? Rick (Humphrey Bogart): If I gave you any thought I probably would. – Casablanca If you work in finance, I bet there is something you use all the time, but … Continue reading
Fast Formulas #3 (Followup): The Derivation
Fast Formulas #3: Pool Average Life with CPR Prepayments presented Formula 3.1., a compact formula for the weighted average life of a homogeneous loan pool assuming a constant prepayment rate. I wrote that the formula took a few pages and “a couple … Continue reading
Fast Formulas #5: QuasiGeometric Series (The Other Trick)
In Fast Formulas #3: Pool Average Life with CPR Prepayments, I described Formula 3.1., a compact formula for the average life of a prepaying loan pool, and I wrote that the formula had been found by using “a couple of … Continue reading
Posted in Fast Formulas, Math, Uncategorized
Tagged Duration, Fast Formulas, Geometric Series, QuasiGeometric Series, Weighted Average Life
2 Comments
Fast Formulas Guide
There is now a handy Fast Formulas Guide at the top of this blog. It summarizes the key formulas and the posts that describe them. The guide may help you see connections between the formulas. By the way, I upgraded … Continue reading
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
Tagged David Hilbert, Fast Formulas, Geometric Series, Math, Matt Henderson
5 Comments
Fast Formulas #3: The Spreadsheet
Fast Formulas #3: Pool Average Life with CPR Prepayments showed a shortcut for finding the weighted average life (“WAL”) of a homogenous pool of loans assuming a constant prepayment rate. The shortcut, Formula 3.1, takes just a few steps to calculate … Continue reading
Posted in Fast Formulas, Math, Spreadsheet Tips
Tagged Average Life Formula, Excel Tables, Fast Formulas, Weighted Average Life
2 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 fixedrate mortgage that pays as originally scheduled. I found this formula (which is probably not original) by substituting the standard level … Continue reading
Posted in Fast Formulas, Math
Tagged Average Life Formula, Closed Formula, Fast Formulas, Financial Math, Loan Average Life, Math, Weighted Average Life
12 Comments