12c Solving for n

[Dieter]

(07-25-2017 10:52 AM)Zac Bruce Wrote:  So I can now see that in my original calculation it is more applicable to the real world to then recalculate FV for n=9, and see what the amount will be, or recalculate for n=8 and make an informed decision whether you are happy to be $9.30 short of your goal of $2500, or wait the extra period and have an extra $214.87

Exactly.

(07-25-2017 10:52 AM)Zac Bruce Wrote:  With the first question, where PMT is involved, it is still important to be able to calculate the final fractional payment. As in when you have loaned an amount of money, it may take 328 payments (n) to fully pay the loan, but it is important to know that the final payment will indeed be a fractional payment (not a fraction of time). Is there anything wrong with the solution given by HP for calculating that final, fractional payment? (i.e. recalculate FV, RCL PMT +)

I'd say this is fine. Especially if this is the way suggested by HP. ;-) You essentially calculate FV as the amount you have overpaid the loan with full 328 payments of $325. So the final payment can be lowered by this.

Here is another approach: Enter n=327 and get PV=$34991,7839. This is the amount you have paid off after 327 periods. So $8,2161 are still missing. For the 328th payment this means you have to pay (1+i)³²⁸ times this, which again is $143,11.

Clear Fin
35000 PV
–325 PMT
10,5 g i
n => 328

327 n
PV => 34991,78
35000 – PV
0 PMT
328 n
FV => 143,11

OK, that's a lot more complicated. #-)

(07-25-2017 10:52 AM)Zac Bruce Wrote:  In place of my original approximate solution (n=327.44), it would instead be interpreted as "327 full payments of $325, plus a final payment of $143.11" and not in terms of time.

I'd say that your approximate result of n=327,4403 may be interpreted as 327,4403 payments, i.e. 327 full and one final payment of 0,4403... times $325 = $143,11.

(07-25-2017 10:52 AM)Zac Bruce Wrote:  The site that Paul suggested included a program to solve for a mathematically correct value of n, which is slightly different to your suggestion (allows for END or BEGIN by storing 1 in either STO 1 or STO 2) but comes up with the same results.

Yes, my little program does only a very basic calculation for this particular case. Real TVM programs do a lot more stuff. ;-)
On the other hand the HP-41 standard pac's TVM program (cf. line 06...20) shows how various scenarios (OK, END mode only) can be handled with one simple formula for n. Here is a translation for the 12C:

Code:

01 RCL FV
02 CHS
03 RCL PMT
04 RCL i
05 /
06 EEX
07 2
08 x
09 +
10 RCL PV
11 LstX
12 +
13 /
14 LN
15 1
16 RCL i
17 %
18 +
19 LN
20 /
21 GTO 00

(07-25-2017 10:52 AM)Zac Bruce Wrote:  I guess if I do the work to internalize and memorize the equation, then yes, very simple! I'm perhaps too blessed to have constant access to electronics and the internet to do the "hard" work for me!

C'mon, this compound interest formula is as basic at it gets. ;-)

(07-25-2017 10:52 AM)Zac Bruce Wrote:  I bought a copy of Gene Wright's book, I think I might go and get it printed and bound tomorrow, start reading and try actually understand the maths, rather than just understanding which buttons to press!

I think there are three levels involved here:
(0) Knowing which buttons to press
(1) Knowing the math behind this
(2) Knowing the meaning of the math. ;-)

Regarding the latter I'm sometimes a bit lost myself.

Dieter