Finance problems (TVM) on hp 49G+ hp 50G Periods and compounds per year are different

[Gil]

Suppose a slightly different problem
as suggested by SlideRule in another post (17B/19B GPM: initial payment)

Assume, for simplication here, that C/YR=P/YR=12 (ie, for the time being, C/YR≠3 as in the previous case).
Let PV=60000, total of years=30, I%YR=12.
The first 12 payments during a full year are, as before, all equal to PMT.
Then, the rules change, with the next 5 years the payments being increased as follows:
the second year, as you are supposed to dispose of a higher income, they increase by 7.5%, so the next 12 payments of the 2nd year will be equal to TVM×1.075;
the 3rd year, the 12 payments will be again increased by 7.5% and then be all equal to (TVM×1.075)×1.075=TVM×1.075²;
the 4th year, (TVM×1.075²)×1.075=TVM×1.075³;
the 5th year, TVM×1.075⁴;
finally, the 6th year (last and 5th increase), TVM × 1.075^5.
Then, up to the end of the reimbursement, all payments remain equal to that last amount TVM × 1.075^5.


Mathematically

PV+
{PMT×1.075^0 × [(v^12-1)/i /(1.01^12)^0)] +
PMT×1.075^1 × [(v^12-1)/i /((1.01^12)^1)] +
PMT×1.075^2 × [(v^12-1)/i /(1.01^12)^2)] +
PMT×1.075^3 × [(v^12-1)/i /(1.01^12)^3)] +
PMT×1.075^4 × [(v^12-1)/i /(1.01^12)^4)] +
PMT×1.075^5 × [(v^(360-12*5)-1)/i /(1.01^12)^5)]
} =0

PV+
{PMT×(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
PMT×[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
}=0,
with v=1/1.01, i=0.01.

Then,
PV+PMT ×
{(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
}=0,
with v=1/1.01, i=0.01


Then,
PMT = -PV /
{(v^12-1)/i ×[Sum, (1.075/1.01)^j, j=0..(5-1)] +
[v^(360-12×5)-1)/i]×(1.075/1.01^12)^5
},
with v=1/1.01, i=0.01,
which gives PMT=-474.825.


Transposition to a more general TVM-Growth HP48-50G Solver program

I transposed the corresponding program, letting it have equally the more usual case without growing payments (I.Growing%=0 or number of Years for the Growing payments YG=0).

To check the case/example of Albert Chan and Karinne in the above post, I included the possibility of having the number of compoundings/year, C.Y, ≠ number of payments/year, P.Y.

Besides, I added here the choice of the payments being made at the end of each period (variable END10=1) or at the beginning of each period (variable END10=0).

Finally, I gave also the possibility of having a remaining global amount FV to be still paid at the very end of the process, ie at the end of YTOT.


Use

Launch the Sover program by pressing its name TVM.G.

Enter, in the Solver, your values followed by the corresponding variable names as follows: 30 YTOT 12 I%Y 12 P.Y 12 C.Y 7.5 IG%Y NEXT-key 60000 PV 0 FV 1 END10.

Then press, always in the Solver, LeftShift P1 to get the value of the payments during the first year.

The following years, the payments will be increased (or not) according to your indications (the several calculations are not included in the result here) until reaching (or not) a constant value P.CST (LeftShift P.CST or RightShift P.CST).


Suppose now that, on the first year, you could afford a payment of maximum 450/month —> PMT =-450

What would be the monthly amounts to be paid on the 2nd year and from year 6/to end of year 30?

Press -450 P1
Press NXT
Press LeftShift IG%Y

You get IG%Y = 9.04416%.
To be paid back monthly in the 2nd year: 450×1.0904416=490.6987
To be paid monthly from year 6 till end year 30:
450×1.0904416^5=693.7845
(or RightShift P.CST and you get also directly, -693.7845, with negative sign indicating that it's a sum to be reimbursed [every month]).