HP49-50G Graduate TVM with/without PMT Growth & C/Yr =/≠ P/Yr + Amortization

[Gil]

Here a directory with 4 programs:

1) TVM.G (Growth/or not of PMT)
2) —>TABLE (formerly called —>AMOR)

3) RESET to be used before NP—>RESULT below
4) NP—>RESULT


1) TVM.G (Growth/or not of PMT)

No Argument, as launching TVM-G will activate the interactive built-in solver for different variables (normally, P1 or FV will be the variable to be solved, but the interest rate, for instance, could be asked for)
NTOT: # of Total payments/periods
I%Y: Yearly nominal rate of interest
C.Y: # of Compounding/Yr (normally, C.Y=P. Y if no mention by the bank)
P.Y: # of Payments/Yr (1...360/365)
YGr: # of Years with payment Growth
NG.Y: "Number" of payments Growth/Yr
(1= payment increase every year, 2 = every 6 months, 3= every 4 months, 4 = quarterly, 6 = every 2 months, 12 = every month, 0.5 = constant for 24 months then P25 to P48=P1*rg; NG.Y must always be <= PY)
PGr%: Rate of the payments Growth related to YGr and NG.Y; definition here was changed in relation to previous versions
(Normally, no Growth: then, put always here 0 (zero) for the Growth rate PGr — and YGr and NG.Y will have automatically a fictive value of 1 with no effect on the results)
PV: Present Value (initial debt/loan; if value zero or same sign as Payment P1, then it's an initial investment, and not a loan, the variable to be solved being then normally FV)
FV: Future Value (remaining debt/loan — generally set to zero when finding PMT P1 for amortisation plan — or final value of the sums invested; always at the end of the Nth period, no matter of the value END10 = 1 <for payments at the end of period> or 0 <payments at the beginning of period>)
END10: normal case when payments at END of period (END10 is true=1) —> enter 1; if payments at begin of period (END10 is false=0) —> enter 0
P1: value of initial payment to be "sent" to the bank, generally to be solved here by the built-in solver (called P1 here, instead of the more common PMT in other programs/applications; but P1 here insists on the very1st PMT, when the payments increase)
r = [(1+ I%Y/C.Y)^C.Y] ^ (1/P.Y); value automatically calculated (normally, you don't ask it to be solved)
rg = 1 +PGr%/100; value automatically calculated
(normally, you don't ask it to be solved)


2) —>TABLE

1 Arg: number of decimal digits for rounding (0, 1, 2...11,12); generally, 2 (2 digits after the comma/unit), or 12 (for 12 digits or no rounding)

Of course, to get the correct, corresponding amortisation table with that program —>TABLE, you should have run before the program TVM.G.

For a loan to be paid back in 30 years with 12 monthly payments, we get a large matrix of dimension 361 × 4, the first row containing the labels 'Payement', 'Int', 'Princ' and 'Bal'. When payments are made at period behin (END10=0), a 5th column 'Bal+Int' (FV) is added. Depending on your memory space, the execution of that program may be not be possible; then, run instead, step by step, the next program NP—>RESULT.


4) NP—>RESULT

You may want to start your amortisation with a group of payments, say 12 once for a full year, then a second cumulative group of 48 payments for the remaining 4 years.

First time, Press RESET program and give always the following two Arg a and b:
a) 2 (for 2 digits rounding; rounding digits in stack level 2 is mandatory after each execution of RESET)
<or put 5 in stack level 2, for a rounding with 5 digits after the dot, or 12 when no rounding at all is wished>
b) 12 (1st group of 12 payments), in stack level 1
& Press NP—>RESULT

And you get, for P1-P12:
sum of the payments (SP)
sum of the interests (SI)
sum of the Principals (SP-SI)
balance

Then, for the 2nd group or 48 payments,
you enter now only 1 Arg, the number of payments in a group:
48 (2nd group of 48 payments payments P13-P60, but without pressing RESET & without mentioning the digit precision) in stack level 1
& Press NP—>RESULT

And you get, for P13-P60:
sum of the payments (SP)
sum of the interests (SI)
sum of the Principals (SPrinc)
balance

For "total of the SP", "total of the SI" & "total of the SPrinc“, read/recall the corresponding values name.

Of course, to get the correct, corresponding amortisation/investment values with that program NB—>TABLE, you should have run previously the program TVM.G.

[Gil]

New version 6

When requiring the evolution table with NB—>TABLE, the "amortisation" table will be adapted if PV is not a loan to be amortized, ie when PV is money initially brought/invested by the client, ie when PV is negative like PMT (or equal to zero), or more precisely when PV × PMT >= 0 (for instance, when deciding for payments PMT to be positive, instead of conventionally negative PMT, and then PV>=0).

For that special situation (not a loan, but an effective investment), when running NB—>TABLE, a column Int.End will be added after Int.Beg if the payments occur at period begin — just for control purposes ; besides, for investment case, the column "Principal" will be suppressed.

The results found here will of course match with the given cases suggested by Werner in his different posts. My thanks again to him for his various calculations and commentaries.

[Gil]

New version 06d

With content of —>TABLE, when launched, duly adapted and corrected for an investment (PMT <0 and PV <= 0, or PMT >0 and PV >=0).