It seems that the series converges if NP < 2A. In other words, the infinite
series gives the interest rate precisely as long as the total payment is
less than twice the amount of the loan.
In the previously mentioned example from Stan Brown's page, we had
P = $200,000, A = $2,800,000 and N = 19, and so NP = 1.36 A approximately;
in the previously mentioned example at the end of the sci.math FAQ entry,
we had P = $50, A = $10,000 and N = 260, and so NP = 1.3 A. This leads me
to suspect that, _for most situations arising in practice_, the series will
This comment will perhaps conclude this thread.
> or mention the form of the general term. He then expressed
> the interest rate as a continued fraction and, by considering
> convergents, obtained "some very excellent approximations". I may
> discuss his and various other approximations in another thread soon.
I will do that, but I don't know how soon.
Nope. One more comment:
I see now that the series was known before Stelson. It was used by
Ralph W. Snyder, C.P.A. in "Schurig's and Baily's Formulae for Finding
the Interest Rate" _The American Accountant_ 17 (Dec. 1932) 362-365.
Perhaps it was also known before Snyder.
BTW, I found Snyder's article to be "amusing". For example, after
mentioning that he was going to use reversion of series, and thinking that
some of the accountants reading his article might not be familiar with
reversion, he says parenthetically
for an example of reversion in detail, see Wentworth's _College Algebra_,
rev. ed., p. 340
Hmm. Just how many "college algebra" texts cover reversion of series