Solving the TVM equation for the interest rate

[Carsen]

(04-15-2018 08:39 AM)Dieter Wrote:  So the result seems to depend on previous input ?!

I believe you are right Dieter. Try this on your HP-12C emulator.

CLEAR FIN
n = 10
PMT = -1,000
FV = 10,000
i = 0.001

If you solve for i, the answer is 2.152976E-11, rather than 0 when you leave the value of i at 0. This proves that since we changed the initial value in i from 0 to 0.001, it changed the result. It's almost like it uses the value in the i register as a initial guess. Just as you concluded before.

I also took the equation of solving TVM problems without an odd period on page 186 of the April 2008 user's guide and played around with it on my HP 50g and HP Prime. The equation is attached to this post. The Prime had to chime in because without a proper initial guess, the 50g would take minutes to solve for i. Also, without an initial guess, the Prime and 50g would get a really big number for a solution. I guess I learned why you needed a initial estimate.

To answer your first question, I think the 1/n estimate would be fine. Every time I used the equation to solve for i on my 50g and Prime solver, the initial guess of 1/n worked FANTASTIC. I was able to solve for i in seconds on my 50g with that initial estimate of 1/n.

I also tried Angel Martin's initial guess equation on my 50g and Prime and it works too. I just had to divide it by 100 to get the percentage as a decimal.

I hope this helps.