HP-12C and the Canadian mortgage factor

Assuming all financial registers are cleared, according to the manual, the keystrokes to calculate the Canadian mortgage factor on the HP-12C are:

 

Key in 6 and press [n ].

Key in 200 and press ENTER , then PV .

Key in the annual interest rate as a percentage and press [+ ], CHS , then FV .

Press [i ].

Clear as mud, so what does that actually do?

 It is using the TVM formula to create the modified mortgage factor for a six month compound regime, prior to running the payment calculation.

 The first instruction places the number of periods, 6 months in this case, into the [n]   register and then 200 is keyed in and enter is pressed and then stored as the present value [PV]. The interest rate is entered, added to the 200 that is on the stack, the sign is changed and then it is stored as the future value [FV]. When [i] is pressed, the HP-12C runs the TVM routine with payment [PMT] as zero and calculates the Canadian mortgage factor.

 Simplified, for our previous interest rate of 6%, it runs the standard TVM calculation with n=6, PV=200, FV=-206, PMT=0 and calculates the modified interest rate to make that so. If the interest rate was 9%, n=6, PV=200, FV=-209, PMT=0 etc

 In the previous example, with the annual interest at 6% the above routine calculates [i] as 0.49386220 for use in the second TVM calculation, so key in number of periods (300) and present value (100,000) and future value (0) and press [PMT] which results in the correct Canadian mortgage payment of -639.81 (note the sign of the payment and present value are always opposite)

The only thing to be wary of is that there is a retained future value of -206 in the register from the manual key sequence and interest rate of 6%, so that has to be zero for the final Canadian payment calculation to be correct.