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

[Albert Chan]

(06-07-2024 07:31 AM)Werner Wrote:  PV*(1+i%/100)^N + PMT*USFV(i%,N) + FV = 0

so if we take N=PYR/CYR, PV=0 and PMT = -i%*CYR, FV will give us I%YR

Too bad HP-12C have different meaning for non-integer N. Why?
Yes, I know N is period, but we can use TVM functionality for other things! Like this trick!

Just to be clear, I%YR here refer to APR (R=CYR)

I would probably multiply by CYR after TVM calculation.
That way, we get I2% = effective rate per (1/CYR year) for free.

I% = 0.414087533 --> I2% = 1.66666667 --> APR(R=CYR) = I2%*CYR = 5.00000001

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Here is another trick, (theoretical) final payment with a 4-banger!

After we solve TVM for PMT, its value likely have fractional cents.
We can't paid fractional cents, and likely use another number, say PMT2

PV/USPV(I%,N) + FV/USFV(i%,N) + PMT = 0

I like to let c = 1/USPV(I%,N), d = 1/USFV(I%,N), because c - d = i

c*PV + d*0 + PMT = 0               // original loan
c*PV + d*FV + PMT2 = 0           // we are paying PMT2 instead, with balance FV
FV = (PMT-PMT2) / d                 // subtract, solve for balance

d = c - i = -PMT/PV - i

Final payment = PMT2 + FV = PMT2 + (PMT2-PMT)/(PMT/PV + i)