The Limits of Analysis

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Some fictions are more ridiculous than others

Men in general are more affected by what a thing appears to be than by what it is, and are frequently influenced more by appearances than by the reality.

- Machiavelli

An account is best described by the amount and timing of its flows.

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 compounding rate from any simple interest rate account for any period. Do it at your own risk. DCF treats simple interest as a two-flow problem, an in-flow and an out-flow. A simple interest account's flow and timing better describes the account.

NOTE: You can't dine out on theoretical flows. DCF can provide a timebase rate (a rate can be calculated on any timebase), for theoretical flows on timebase-time, for any account. (On a 365-day timebase, by default, using XIRR.) The problem with a DCF analysis returning a rate for a simple interest account (with a period shorter or longer than timebase time) is that a simple interest account has no flows at timebase-time.

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A discounted cash flow two-flow annual-timebase rate extraction:

Given:

I=PR, a simple interest account, i. e., one period

$100 principal

10-year period

100% rate, i. e., doubling your money to $200

 

Discounted Cash Flow, 2 flows (spreadsheet notation)

APY = 100*((outFlow/inFlow)^(timebase/timeBetweenFlows)-1)

APY = 100*((200/100)^(365/3650)-1) = 7.177346

 

Proof: Reverse-engineer the DCF (compound interest):

inFlow*(1+%RateAnnual/100)^(time/timebase) = outFlow

  $100*(1+7.177346/100)^(3650/365) = $200

Notes:

1. A rate can be stated on any timebase.

2. Time and timebase must be stated in the same units.

3. 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 reality.

Men have become tools of their tools.   - Thoreau