(12C) Annualised Equivalent Rate & Continuously Compounded Rate

[Joe_H]

Often the interest rate given is the nominal rate that compounds a given number of times in the year. I want a very quick way to calculate the annualised equivalent rate (AER) which is the same rate that compounds only once a year (often this is what banks quote as regulatory authorities mandate them to as the public understand 8.3% AER versus 8% APR compounded, say, monthly during the year. Also options and some other derivatives use the continuously compounded rate CCR (the asymptotic limit going from compounding once a year to monthly, to weekly, to daily, to hourly etc.). So the program will also calculate this also. I want to avoid using other registers, if possible, so it's a bit longer than necessary (e.g. the 100's being entered below!) as I don't want it to disturb a cashflow sequence entered into the calculator. {I'm intending to attempt the CFA exams and anything that adds to speed is a good :-) Can't figure out how to post smiley's to this! :-( }

The other permitted calculator (TI BA II Plus) has a sheet to do this but the HP12C will have significantly lower keystrokes as only have to input n (number of compounding periods per year) and i (the nominal rate) and then R/S. TI doesn't calculate the CCR on that sheet.

AER is output to X and CCR to Y.

For example (rounded to 2 decimal places):
i = 8% APR compounded monthly
AER = 8.30%
CCR = 8.33%

Let me know if you spot any problems in it.

Regards,

Joe

Code:


01 1
02 RCL [i]    
03 %
04 ENTER
05 e^x
06 x<>y
07 Rv
08 -
09 CHS
10 1
11 0
12 0
13 x
14 Rv
15 Rv
16 RCL [n]
17 /
18 1
19 +
20 RCL [n]
21 y^x
22 1
23 -
24 1
25 0
26 0
27 x
28 x<>y
29 Rv