The Limits of Analysis
- or -
Some fictions are more ridiculous than others
Men in general are more affected by what a
thing appears to be
An account is best described by the amount and timing of its flows.
than by what it is, and are
more by appearances than
by the reality.
Only accounts with flows at equal periods, at a constant rate, are well
described by a single number - typically, savings and loan accounts. All
other accounts, including simple interest accounts with long periods (simple
interest is the basic building block of compound interest accounts), are not
well described by a single number.
I=PRT's logically dubious method, using time-geometric, can extract an annual
rate from a simple interest rate with a period longer than one year.
Discounted cash flow [DCF], using time-exponential, can extract an annual rate
from a simple interest rate that has a period longer than one year. Do it at
your own risk: a simple interest account's flows and timing better describe
DCF treats simple interest as a two-flow problem, an
in-flow and an out-flow. DCF
can provide an annual rate (though a rate can be
calculated on any timebase), for theoretical flows, at
timebase-time, compounded annually. The problem with a
DCF analysis of simple interest is that simple interest
has no flows at timebase-time. You can't dine out
on theoretical flows.
Just because you can reverse-engineer a simple interest rate to an annualized
compound rate, that doesn't mean that you have a useful description of the
simple interest rate account. The real flows for $100 at 100% interest,
10-years, are very different from the hypothetical flows for $100 at 7.177346%
interest compounded annually. There is no compounding in a simple
interest account. The 7.177346% rate is a simulation, not a representation, of
A discounted cash flow two-flow annual-rate extraction:
- I=PR, a simple interest account (i. e., one period)
- $100 principal
- 10-year period
- 100% rate
- Discounted Cash Flow, 2 flows (spreadsheet notation)
- APY = 100*((outFlow/inFlow)^(timebase/timeBetweenFlows)-1)
- APY = 100*((200/100)^(365/3650)-1) = 7.177346
- Reverse-engineer the DCF (compound interest):
- inFlow*(1+%RateAnnual/100)^(time/timebase) = outFlow
- $100*(1+7.177346/100)^(3650/365) = $200
- 1. A rate can be stated on any timebase.
- 2. Time and timebase must be stated in the same units.
Men have become tools of their tools. - Thoreau