Looking for TVM formulas

[Dieter]

(04-01-2014 08:01 PM)Dave Britten Wrote:  EDIT: Sweet, that was pretty easy. I'm now getting FV = -333,783.3499506 when I calculate the Susan problem. My 48SX Equation Library card returns -333,783.349948. I'm fine with that incredibly small error (I suspect the 48 is using extended reals in SysRPL for greater accuracy).

I assume there is another reason. Like various other HPs, the 48/49/50 series has a dedicated ln1+x command which is incredibly helpful here. And these machines also feature a special e^x-1 command that will help here as well - just take a look at the formula:

Code:

    FV  =  PMT * (( (1+i/n)^n)-1) / (i/n)
    use ln1+x here   ^^^^^
    and e^x-1 there        ^^^^^
=>
    FV  =  PMT * n / i * e^x-1[n * ln1+x(i/n)]

It's these two matching commands that make the calculation exact.

Evaluating ln(1+x) is pretty easy, a simple way is shown in the mentioned Advanced Functions Handbook. However I do not know of a straightforward method of determining e^x-1. Any suggestions?

Determining the interest rate i requires a numerical solver. Finding a valid solution as well as doing so quickly deserves a closer look at the initial guesses for i. Here you might want to read an earlier thread where this topic has been discussed in detail. You can find it here, especially message #14 ff. You should also take a look at "fhub"'s TVM solver for the 34s and other platforms which has been discussed in the old forum as well.

Dieter