(12C) Actuarial Calculations

05122018, 05:41 AM
(This post was last modified: 05122018 06:33 AM by Gamo.)
Post: #1




(12C) Actuarial Calculations
Since HP 12C always calculate [n] as an Integer with rounding up result.
Program below help solve this problem to get result with fractional part and [n] can be input with fractional part by using the Actuarial Method. *Program to calculate [i] and use fractional [n] Code:
Example of calculating interest rate required for growth: A savings account has a balance of $1000. What annual interest rate is required to double the money in 5½ years? Store 0 in register 0 for END mode; store 1 in register 0 for BEGIN mode. 0 STO 0 > 0 // Set END mode 1000 CHS [PV] > 1000.00 2000 [FV] > 2000.00 5.5 [n] > 5.50 0 [PM]T > 0.00 R/S > 13.43 // Answer *Program to calculate [n] Code:
Example of calculating compound interest: A deposit of $150 is made each month in an account paying 6.5 percent, compounding monthly. How long will it take to accumulate $20,000? Assume END mode. Store 0 in register 0 for END mode; store 1 in register 0 for BEGIN mode. 0 [STO] 0 > 0.00 6.5 g [i] > 0.54 0 [PV] 150 [CHS] [PMT] > 150.00 20000 [FV] > 20000.00 [R/S] > 100.63 This program is from HP Support website. https://support.hp.com/usen/document/bpia5043 Remark: All calculations above work on HP 15C using TVM program from the Advance Functions Handbook. For HP12C these two program together use about 95 steps this can enhance 12C TVM functions. Gamo 

05122018, 07:00 PM
Post: #2




RE: (12C) Actuarial Calculations
(05122018 05:41 AM)Gamo Wrote: *Program to calculate [i] and use fractional [n] This seems to be a Newtonstyle solver that calculates the interest rate iteratively. This requires the usual convergence check: exit if the absolute value of the last change in i is less than 1E–8. Now take a look at line 53...56: here the HP programmer found a nice way to determine the absolute value of x. Code: 53 ENTER Compared with the common method (calculate √x²) this has three advantages: there are no roundoff errors, LastX is preserved and it also works for x ≥ 1E+50. (05122018 05:41 AM)Gamo Wrote: Remark: Just to be clear – I assume what you want to say is this: Unlike the 12C, the TVM program in the 15C Advanced Functions Handbook does not round n to the next higher integer, it directly returns a fractional results if required. So the above programs are not needed there. Dieter 

06112019, 02:40 PM
Post: #3




RE: (12C) Actuarial Calculations
(05122018 05:41 AM)Gamo Wrote: Since HP 12C always calculate [n] as an Integer with rounding up result. Gamo As far as I can make out the HP12C does use noninteger n for i calculation. The only difficulty is calculating a noninteger n. I tried it on mine and got the correct i value for a noninteger n. For example: PV = 100 FV = 111.10 (PMT=0) n = 1.1 i calculates as 10% which is correct But: PV = 100 FV = 111.10 (PMT=0) i = 10% n calculates as 2 which is the problem. The TI BAII Plus (other permitted CFA calculator) does calculate n correctly for these TVM inputs. As far as I can make out the first program (and longer one) isn't required but the second one is useful and I'll try it now. Joe 

06112019, 02:50 PM
Post: #4




RE: (12C) Actuarial Calculations
Thanks Gamo,
That works fine (I'll probably change the registers where the interim values are stored so as not to affect a cashflow already in the calculator). The n value before calling the program needs to be lower than the calculated value or it overflows. Setting it to zero is the best bet before calling the program. Joe 

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