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

[Gil]

Solution with the HP50G:

1) Use the finance application of the calculator, with the explained example of Albert Chan
(the summary of the 3 steps/calculations below for nominal I%YR are in bold)
2) However, instead of the initial nominal interest of 5% to be normally put in I%YR, calculate the corresponding nominal interest x, as follows:
a) Effective/real interest, relative to Compounding, for the fractional period:
5/100 / (C/YR) = 0.05/3 —> effective/real interest for 4 months = 1.667%
b) Now, calculate, always relative to the Compounding, the effective yearly interest:
(0.05/ C/YR +1)^(C/YR) = (0.05/ 3 +1)^ 3 =1.050837 —> effective real interest = 5.0837%
c) Then calculate the corresponding effective/real interest for the fractional period, relative to the Payments = 1/(P/yr) = 1/12 (ie here for 1 month):
1.050837^(1/ P/YR)=1.050837^(1/ 12)= 1.004140875 —> effective/real interest for 1 month Payment = 0.4140875%
d) Now, put in I%YR the corresponding value x (nominal yearly interest) instead of the initial nominal yearly 5%:
x=(1.004140875-1)* P/YR *100=(1.004140875-1)*12*100 = 4.969050384 for I%YR
3) Complete 60 for N, copy if necessary the above value x = 4.969... into I%YR, 30000 for PV, 12 for P/YR (that is available here!)
4) And go to PMT line and press SOLVE
to get -565.711726419.