Joined: 10 Jul 2022
Location: United States
|Posted: Sat Jul 30, 2022 8:27 pm Post subject: First Impressions from a New Curta Owner
|After my earlier post, I was able to obtain a type 2 in fabulous condition thanks to a helpful individual on this board. I've had it for a couple of days now, and thought I would post with my impressions thus far.
I am an actuary by trade and I wanted to see if I could put the Curta to work in a real-life scenario. I work on private employer pensions, so that will inform the types of calculations I am performing here.
The type 2 has a nice weight to it and feels good in the hand. It is slightly too large for me to be able to comfortably manipulate the carriage with my left hand while also holding it. Maybe this will just take some more practice, but I can see the appeal of the type 1 in that regard (maybe I need a type 1 now too!).
It is easy while turning the handle quickly to accidentally move just a hair past the zero point. The instinct is to try to move it back, which of course is a terrible idea. You have to complete the next turn, then make a minus turn. This is something I need to very carefully train myself to do.
It did get "stuck" at one point while I was working with it. I panicked—did I just break my beautiful machine? After a little gentle wiggling it came un-stuck and it has not happened again. But that minute or so was pure terror.
Scenario 1: Average Salary
A pension plan might say that an employee's benefit is a percentage of their 3-year average salary. With the employee's salary history in front of me, I can usually scan it visually and pick out the consecutive years with the highest average (most often the 3 most recent years). Then it's straightforward to add those salaries together on the Curta, and divide by 36 (since I want a monthly amount) using the subtractive method.
This was one of the first practical examples I tried and it was easy and quick on the Curta.
Scenario 2: Cash Balance
A popular type of pension gives employees a "hypothetical" retirement account. This account is increased each year with interest at a given rate, plus a contribution credit which might be a percentage of the employee's annual salary. In this case I want to be able to verify the employee's ending hypothetical balance, given their beginning balance, interest rate, and salary.
I started by entering their salary into the SR, and multiplying it by the contribution percentage, say 2.5%. This produces the contribution credit amount, which I would note down for later.
Then I cleared the RR and CR, entered the beginning balance on the SR and multiplied by the interest crediting rate, for example 4%. That gives the amount of the interest credit. Move the carriage over 2 spots and multiply by 1, that adds the beginning balance to the interest. Now I would re-set the SR to the contribution credit that I calculated before, and with the carriage in position 1, make 1 turn to add it. This gives me the ending hypothetical account balance.
This method is straightforward and not terribly time-consuming. However I wonder if there is a way that I can eliminate the intermediate step of writing down the contribution credit. I will continue to experiment with this and see if I can come up with something better. Ultimately this problem is just calculating (a x b)+(c x d) in a single step, and I think there must be a better way.
Scenario 3: Accumulating with interest
If an employee is currently age 51, and we assume he will retire at age 62, what will his account be worth at retirement? With an interest rate of 4%, the future value is simply equal to the present value multiplied by 1.04^11, since the employee has 11 years to retirement.
The suggested method for doing powers is the serial multiplication method, however that runs out of available digits very fast. What I ended up doing was what the Computing Examples manual calls "Extended Rule of 3"—basically, multiplication followed by division, followed by multiplication, followed by division, etc. This allowed me to control the precision of my calculation effectively, since the least significant figures get dropped when doing the division. The process was to start with 104 x 104, giving 10816 on the RR, then clear the CR and divide by 100 using the subtractive method giving 10816 on the CR, then re-set 104 on the SR and leaving the reversing lever down, reduce the CR to 0 by making positive turns which would put 104^3 or 1124864 on the RR, and repeat this process as many times as necessary. I used the decimal point markers to keep track of how many powers I had done. I did not worry too much about keeping track of the decimal points in my calculations since it would be obvious where they go at the end.
Once the needed power has been calculated on the CR, I can enter the present value of the account on the SR and then reduce the CR to 0 with positive turns to the get the future value on the RR.
This process is accurate and effective, but very time-consuming. For powers of 4 or 5 or 6 it wouldn't be so bad, but I wouldn't want to do it for 30 or 40.
Other things I want to try:
Discounting at interest—this is basically the opposite of accumulating that I discussed in the previous section. I can think of a few ways I might approach it; either calculating the inverse of (1+i) and then accumulating that, or accumulating (1+i) and then taking the inverse of the accumulated product, or accumulating (1+i) and then dividing the amount by the accumulated product. I will have to experiment and see what works best.
Odd-period interest—for when a payment occurs not exactly an even number of years from the start date. While I know there are ways to do non-integer exponents on the Curta, I might rely on the so-called "Banker's Rule" which says to use simple interest for periods of less than 1 year. That should make the calculation much easier.
Date calculations—related to the previous item, if a payment is made on an odd date, what is the best way of calculating the fraction of the year for which interest applies? I have some ideas but I will need to experiment.
There is no practical reason anyone should be using a Curta for real work in 2022. We all have supercomputers in our pockets, not to mention Excel spreadsheets and cloud computing that can solve any problem you might need to compute in a far faster and more efficient manner than a Curta.
So, if you are even considering it (like me), you must be a little weird or just have a thing for old technology. If you already have an HP Voyager series calculator on your desk, a Curta might make a good addition.
For me, I will probably not use the Curta as a primary calculating device, but I can see myself picking up the Curta to check the results calculated by our software in some cases. Some things, like accumulation with interest as I mentioned, are simply too burdensome to perform on the Curta on a regular basis. For others, especially things like adding a set of values or doing a percentage calculation, I think I will grab the Curta as often as not. The tactile experience of it is just really wonderful; it is a real pleasure to hold and to operate. I'm looking forward to getting to know the device better over the coming weeks and months.
Last edited by cbzero on Mon Aug 01, 2022 1:19 pm; edited 1 time in total
Joined: 27 Oct 2009
|Posted: Sun Jul 31, 2022 7:48 am Post subject:
|Thanks for your first impressions - what a detailed report!
It clearly shows that a Curta was originally a computing device used in various professional applications - today, unfortunately, in 99% of all cases a collector's item without the actual purpose. Furthermore, a Curta that is used daily runs much better than a Curta that was unused for years (even if it is in the much quoted "perfect condition"...).
The report motivates to use your own Curtas a little more - exercise in the fresh air is good...
Who uses his Curta daily? - which calculation tasks are solved with it?
:: m u r f f
Joined: 18 Apr 2013
|Posted: Sun Jul 31, 2022 10:51 am Post subject:
|I enjoyed reading your report very much, thanks. When our kids were younger they would regularly use a Curta to check their mathematics school work calculations.
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