17BII, 27S: doing TVM calculations inside solver equations

04302019, 03:04 PM
Post: #1




17BII, 27S: doing TVM calculations inside solver equations
For whatever reason, the 17BII and 27S don't seem to have solver functions for calculating TVM variables, while the 19BII has N(), I%YR(), PV(), PMT(), and FV().
Is there any good way to mimic those functions inside a solver equation on the models that don't have them? I have a formula where I need to be able to calculate both N (where FV=0; PV, PMT, and I% are nonzero), and subsequently FV (using a new value for N) as part of the intermediate results. Do I just need to rearrange the TVM formula given in the manual's appendix? 

04302019, 07:44 PM
Post: #2




RE: 17BII, 27S: doing TVM calculations inside solver equations
(04302019 03:04 PM)Dave Britten Wrote: Do I just need to rearrange the TVM formula given in the manual's appendix? Probably the best way is just that. Access to the TVM functions in the solver is the key feature that separates the 19B/19BII (don' recall about 18C, but probably it has them too) from all the 17's and 27S. I suppose the Memo function (and truly much easier to use alpha keyboard) is generally seen as the 19B family 'killer app' but only until you try to use it much. IIRC, even using the provided formulas will produce slightly different results than manually using the builtin TVM, probably because the TVM code has some twekas for corner cases, and preserves accuracy in iterative calculations. Bob Prosperi 

04302019, 08:21 PM
Post: #3




RE: 17BII, 27S: doing TVM calculations inside solver equations
(04302019 07:44 PM)rprosperi Wrote: IIRC, even using the provided formulas will produce slightly different results than manually using the builtin TVM, probably because the TVM code has some twekas for corner cases, and preserves accuracy in iterative calculations. The main issue would be trying to solve for n, since the TVM formula uses USPV(i%:n) and SPPV(i%:n) internally. I'm thinking it's probably more trouble than it's worth to make this work on a 27S, and I'm better off sticking to true programmable financial calculators  like my DM42 or Casio fc200  for this kind of interest savings problem. 

04302019, 08:32 PM
(This post was last modified: 04302019 08:32 PM by Csaba Tizedes.)
Post: #4




RE: 17BII, 27S: doing TVM calculations inside solver equations
1.) If you solve the TVM equation for N and your FV is zero why the FV will change when you calculated FV using the new N?
2.) I do not really understand your question: (04302019 03:04 PM)Dave Britten Wrote: ... calculating TVM variables ... OR ... mimic those functions?Because 17BII has TVM functions in Solver and the Appendix B of Manual TVM section includes the calculation (with USPV and SPPV). Type in the Solver and use it  or use the TVM menu. (I guess I do not understand something  an example here, please!) Csaba 

05012019, 12:58 PM
(This post was last modified: 05012019 01:02 PM by Dave Britten.)
Post: #5




RE: 17BII, 27S: doing TVM calculations inside solver equations
I'll explain the specific problem in more detail, in case there's an easier way to do it that doesn't involve TVM.
I'm trying to make a solver formula that will calculate the amount of interest saved over the remaining life of a loan if I were to make an extra principal paydown of a given size. This is the general calculation process that I use: 1. Make sure N, I%, PV, PMT, and FV reflect the current (or opening) state of the loan. 2. Subtract the extra principal payment from PV, and update PV. 3. Recalculate N to determine the new number of payments remaining to pay off the reduced principal. This will probably be a noninteger value, i.e. an odd payment at the end. 4. Recalculate FV using FLOOR(N) to determine the remaining balance for the final odd period. 5. Calculate the total interest paid on the original principal using the original values in "N*PMT+PV" (gives a negative value representing total interest paid). 6. Calculate the total interest paid on the reduced principal, using the new values of N, PV, and FV in "PMT*FLOOR(N)+FV*(1+I%/100)+PV" (multiplies the payment amount by the number of full payments, and calculates the periodic interest on the final odd period). 7. Subtract the original interest (step 5) from the reduced interest (step 6) to obtain the total savings (a positive number). As an example, suppose you've got a loan with these properties: N=360 I%/YR=4.75% PV=141,000 PMT=735.52 FV=0 The total interest payments on the loan would be ($123,788.19). If you paid an extra $1,000 in principal, then N becomes 354.41, and the total interest paid is ($120,679.83), giving a total savings of $3,108.36. Here's the program I have on my DM42 for calculating this. It relies on my TVM program, which isn't listed here, but it should be fairly obvious how it's used in this example: XEQ "N" and XEQ "FV" recalculate the respective TVM variables, updating the variable directly, and also leaving the new value in X, lifting the stack. Also, XEQ "SS" is a stacksave routine, and XEQ "R_YZTX" restores the saved stack, but keeps whatever value was in X at the time it's called (represented by the underscore), and puts the old value of X into L (so it's the same stack behavior you would see from singleargument functions like LN). I've added a few comments to the code. Code: 00 { 163Byte Prgm } I have this algorithm implemented on many different calculators (DM42, HP 200LX solver, Casio fc200, Casio fx9860G  both as a program and a spreadsheet, and a version for any old Casio scientific with array memories, covering the fx7000G through fx9700GE, which also requires a TVM program I wrote), but it would be nice to have it on my 17BII since it's a financial calculator. 

05012019, 02:28 PM
(This post was last modified: 05012019 02:36 PM by Csaba Tizedes.)
Post: #6




RE: 17BII, 27S: doing TVM calculations inside solver equations
(05012019 12:58 PM)Dave Britten Wrote: I'll explain the specific problem in more detail, in case there's an easier way to do it that doesn't involve TVM. Two notes to this:
Therefore in real life the good solution to calculate the required periods to reduce the PV below your monthly payment, and then you can pay the whole PV. So, you need to make a table: 1st Coloumn: Your prepayment (eg. in every 6 periods or every 12 periods), 2nd Coloumn: The required N for reducing PV<=PMT With this table you can easily decide what is the preferred prepayment or N for you. Csaba 

05012019, 03:36 PM
Post: #7




RE: 17BII, 27S: doing TVM calculations inside solver equations
(05012019 02:28 PM)Csaba Tizedes Wrote: Two notes to this: Sounds like loans are handled a bit differently between Hungary and the US, then. Whenever I make an extra principalonly payment (which I've done a couple of times), the outstanding balance is directly reduced, but the payment amount doesn't change. This means that the loan will be paid in full sooner, and thus collect less total interest. When I did this for my mortgage, I had the option of having the loan reamortized to the same length, which would have lowered the monthly payment, but would not have reduced the total interest paid by as much as leaving the payment amount at its original higher value, and settling the loan earlier. 

05012019, 03:45 PM
Post: #8




RE: 17BII, 27S: doing TVM calculations inside solver equations
(05012019 03:36 PM)Dave Britten Wrote: Sounds like loans are handled a bit differently between Hungary and the US, then [...]Yes, but when you prepayed your debt (in Hungary) the remaining loan recalculated and the interest also reduced! And if your principal is small enough to pay the whole in one amount, the remaining periods interest is zero, of course, no need to pay. Csaba 

07062019, 01:00 AM
Post: #9




RE: 17BII, 27S: doing TVM calculations inside solver equations
Dave,
wouldn't it be easier to use some of the existing SOLVER examples for WrapAround Loans or Extra Payments  or Skipped Lease Payments  as inspirating starting points? (All programs are in the support docs on the Museum DVDs) Then you can use any point in time during the life of the loan to add an extra payment an calculate your total interest savings. Best regards, Peter (05012019 12:58 PM)Dave Britten Wrote: I'll explain the specific problem in more detail, in case there's an easier way to do it that doesn't involve TVM. 

07062019, 01:53 PM
Post: #10




RE: 17BII, 27S: doing TVM calculations inside solver equations
(07062019 01:00 AM)Peter A. Gebhardt Wrote: Dave, That's a good idea, maybe I'll dig into those books and see how they approached it. 

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