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Dieter · (This post was last modified: 07-24-2017 03:31 PM by Dieter.)

Note: edited to address some more questions.

(07-24-2017 11:27 AM)Zac Bruce Wrote: To then make the answer correlate with other financial calculators I came up with the following;
(with the -143.11 still on screen)
RCL PMT X><Y %T (44.03) e.g. .4403 of a total payment.
So the answer is 33.44, which is what other calculators report.

?!? Where do you get this 33,44 from? I'd say this is 327 full periods plus 0,4403 = 327,44 periods.

But this is only an approximate answer, it is a linear interpolation of a nonlinear function. The true result here is not 327,4403 but 327,4393. Rounded to two decimals the difference in this particular case does not show up. But don't try this with smaller n. Anyway, at least you get an approximate result.

(07-24-2017 11:27 AM)Zac Bruce Wrote: However, when a PMT value is not involved, I can't find a simple way of performing the same calculation. My maths just isn't strong enough.
e.g. PV 1250, FV 2500, i=9% compounded annually, solve for n?
12c gives 9, and when you re-solve for FV it gives 2714.87
Other calculators will give n=8.04

Without PMT the solution is trivial. If you really need the fractional answer for n this can be calculated directly, either manually or with a small program:

RCL FV
RCL PV
/
CHS
g LN
1
RCL i
%
+
g LN
/

For the example this yields n = 8,0432.

Of course you can always use your own little program for calculating n without rounding up to the next higher integer. The formulas are known, so just "code your own". ;-) As shown, the PMT=0 case is trivial, but even with PMT the formula is quite simple. For your example (no FV, "end" mode assumed) and i decimal (i.e. 0,00875 here) n = – ln(1 + i·PV/PMT) / ln(1+i).

(07-24-2017 11:27 AM)Zac Bruce Wrote: Is there a simple way to calculate what the 714.87 represents in terms of time?

What 714,87? I just see 2714,87 which is the FV after 9 periods.

Dieter