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Solving the TVM equation for the interest rate
04-19-2018, 09:45 PM (This post was last modified: 04-19-2018 09:59 PM by Dieter.)
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RE: Solving the TVM equation for the interest rate
(04-19-2018 02:56 PM)Jeff_Kearns Wrote:  The 15C program is an adaptation of the Pioneer's (42S/35S/33S/32Sii/32S) Accurate TVM routine, ...

If I remember correctly this implies the use of ln(1+x) and exp(x)–1 for a more correct calculation without digit cancellation.

(04-19-2018 02:56 PM)Jeff_Kearns Wrote:  I may be missing the point of this thread, and apologize if that is the case. If it is, can someone please explain the issue.

Simply read the first post. ;-)

The discussion is about the way an initial estimate for the iterative interest rate calculation is determined. It should be reasonably close to the true result and lead to the final solution in not too many iterations.

For the FV=0 case (cf. the above mentioned program in the 11C manual) an estimate of |PMT/PV| – |PV/PMT|/n² was proposed. This indeed is a good first guess for this particular case, as it has two nice properties:

First, if –FV = n·PMT the interest rate is zero, and in this case the estimate is zero as well. Second, as n gets larger and eventually approaches infinity, the interest rate approaches the limit |PMT/PV|, which is also true for the estimate. Between these two limits the estimate seems reasonably close to the true result (at least in the cases I tried), so the estimate works well for interest rates ≥ 0. However, in cases where the interest rate is negative the estimate can be significantly off. But at least the first one or two iterations usually get it back on track.

So this works quite well for this particular case where FV=0 and i≥0. On the other hand, the estimate I proposed is more universal as it considers both PV and FV. If I did the math correctly, it agrees with the true result at i=0 and n=1. As n increases the estimate is slightly high, but close, and it seems works very well. For very large n this estimate finally approaches 2x the true result. Maybe this can be improved by tweaking the formula a bit.

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RE: Solving the TVM equation for the interest rate - Dieter - 04-19-2018 09:45 PM

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